In a group of graduate students over the age of 30, 70% of male studen

Question

In a group of graduate students over the age of 30, 70% of male students have secured a job after graduation and 82% of female students have secured a job after graduation. Which of the following could be equal to the percentage of graduate students over the age of 30 who have secured a job after graduation?

A. 68%
B. 70%
C. 76%
D. 82%
E. 85%

A. 68%
B. 70%
C. 76%
D. 82%
E. 85%

pushpitkc · Answer

Easiest way to solve such problems is to assume numbers.
Let there be 50 male and 50 female students over the age of 30 in the group.

70% of the male students ( 0.7*50 = 35 ) and 82% of the female students( 0.82*50 = 41 ) secure a job.

Therefore, the number of graduate students who secure a job is 76(35+41) and a percentage is  \frac{76}{100} = 76 %  (Option C)

Bunuel · Answer

Since the overall average must be between the individual averages, then the only acceptable answers is C.

Answer: C.

D3N0 · Answer

Ans: C 
Why although number of students male female are not given we know the % age of those who secured job. because 70% of male and 82%of female secure the job. we can take many pairs of estimated numbers of male and female the %age for the total graduate to the total will always fall between 70% to 82%. not 70% and 82% because then we have to take no. of male to be 0 for the latter or no of female to be 0 for former. 
hence there is only one ans which lies between 70% and 82%. = 76%
Ans : C

akadiyan · Answer

This problem is easy to solve using numbers

Take Male and female both as 100

Male: 70% - 70
Female - 82% - 82

Total 152/200 - 76%

Ans : C

Edited this post based on observation made by  pushpitkc

GMATBusters · Answer

This is a Question based on weighted Averages, the combined average depends on the number of Male and female students.
But one thing is sure that the  combined average is always between individual averages. 
hence we have to select the values from the option which is between 70 and 82 is 76.
OA = C.

PS : 
1) Putting the values of male and female as numbers might not be the correct approach for this question, as the combined average depends on the ratio of male and female students.
If the answer option were 71 instead of 76, then 71 would have been the right answer.
2) if someone wants to know the proof that combined average shall be between 70 & 82, please see the sketch.

ScottTargetTestPrep · Answer

Since we know that there are male and female students, the percentage of students who have secured a job must be between 70% and 82%, so a possible percentage is 76%.

Answer: C

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In a group of graduate students over the age of 30, 70% of male studen

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