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

Question

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

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

PKN · Answer

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)

globaldesi · Answer

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

JeffTargetTestPrep · Answer

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards