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

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
Of the female students at Barkely University, 5/6 are on the honor rol  [#permalink]

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17 Aug 2018, 12:00
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Difficulty:

25% (medium)

Question Stats:

84% (01:42) correct 16% (02:39) wrong based on 38 sessions

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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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17 Aug 2018, 12:14
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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17 Aug 2018, 12:24
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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20 Aug 2018, 11:16
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.

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Re: Of the female students at Barkely University, 5/6 are on the honor rol &nbs [#permalink] 20 Aug 2018, 11:16
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# Of the female students at Barkely University, 5/6 are on the honor rol

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