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Of the female students at Barkely University, 5/6 are on the honor rol

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Of the female students at Barkely University, 5/6 are on the honor rol  [#permalink]

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New post 17 Aug 2018, 11:00
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Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what fraction of all the students are on the honor roll?

A) 5/9
B) 3/15
C) 23/30
D) 43/60
E) 53/90

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Re: Of the female students at Barkely University, 5/6 are on the honor rol  [#permalink]

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New post 17 Aug 2018, 11:14
Bunuel wrote:
Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what fraction of all the students are on the honor roll?

A) 5/9
B) 3/15
C) 23/30
D) 43/60
E) 53/90


Let the total student is 100
#Female students=\(\frac{3}{5}*100\)=60 . So, #male students=40
# female students in Honor roll=\(\frac{5}{6}*60\)=50
# male students in Honor roll=\(\frac{2}{3}*40\)=\(\frac{80}{3}\)
Total#students in honor roll=50+\(\frac{80}{3}\)=\(\frac{230}{3}\)
Fraction of students in the honor roll=\(\frac{230}{3*100}\)=\(\frac{23}{30}\)

Ans. (C)
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Of the female students at Barkely University, 5/6 are on the honor rol  [#permalink]

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New post 17 Aug 2018, 11:24
Total students = 5x
Female = 3x;
Male = 2x;
honor on roll female = \(\frac{5}{6} *3x\) = \(\frac{5x}{2}\);
honor on roll male = \(\frac{2}{3}\)*2x= \(\frac{4x}{3}\);
hence total on roll = \(\frac{5x}{2}\) +\(\frac{4x}{3}\)= \(\frac{23x}{6}\);
total students were 5x;
there total on roll = \(\frac{23x}{6}*\frac{1}{5x}\);
= \(\frac{23}{30}\);
ans C
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Re: Of the female students at Barkely University, 5/6 are on the honor rol  [#permalink]

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New post 20 Aug 2018, 10:16
Bunuel wrote:
Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what fraction of all the students are on the honor roll?

A) 5/9
B) 3/15
C) 23/30
D) 43/60
E) 53/90


We can let the number of students = 120.

Thus, 3/5 x 120 = 72 are female, and 120 - 72 = 48.

So 72 x 5/6 = 60 female students are on the honor roll, and 48 x 2/3 = 32 male students are on the honor roll.

Thus, (60 + 32)/120 = 92/120 = 46/60 = 23/30 are on the honor roll.

Alternate Solution:

Since 3/5 of all students are female, we see that 5/6 x 3/5 = 3/6 = 1/2 of the total students on the honor roll are females. Similarly, since 2/5 of all students are male, we see that 2/3 x 2/5 = 4/15 of the total students on the honor roll are males. Thus, the fraction of all students on the honor roll is:

1/2 + 4/15 = 15/30 + 8/30 = 23/30 of all students are on the honor roll.

Answer: C
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Re: Of the female students at Barkely University, 5/6 are on the honor rol &nbs [#permalink] 20 Aug 2018, 10:16
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