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

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Intern
Joined: 19 May 2015
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In 1996, 80% of the students at University Y were undergraduates  [#permalink]

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30 Jun 2017, 12:50
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Difficulty:

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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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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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 $$= \frac{64}{100} = \frac{16}{25}$$

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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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