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A professor gave the same exam to two classes. The 200

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Senior Manager
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A professor gave the same exam to two classes. The 200 [#permalink] New post 19 Jun 2008, 04:03
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A professor gave the same exam to two classes. The 200 students in the first class scored an average (arithmetic mean) of a 75 on the exam. The students in the second class scored an average (arithmetic mean) of an 85 on the exam. If the average (arithmetic mean) score of students in both classes was a 77, how many students are in the second class?

A. 50
B. 75
C. 150
D. 64
E. 80
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Re: PS: Average [#permalink] New post 19 Jun 2008, 04:44
lexis wrote:
A professor gave the same exam to two classes. The 200 students in the first class scored an average (arithmetic mean) of a 75 on the exam. The students in the second class scored an average (arithmetic mean) of an 85 on the exam. If the average (arithmetic mean) score of students in both classes was a 77, how many students are in the second class?

A. 50
B. 75
C. 150
D. 64
E. 80


A.50

200*75 + x*85 = 77(x+200); x = 50
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Re: PS: Average [#permalink] New post 19 Jun 2008, 04:57
lexis wrote:
A professor gave the same exam to two classes. The 200 students in the first class scored an average (arithmetic mean) of a 75 on the exam. The students in the second class scored an average (arithmetic mean) of an 85 on the exam. If the average (arithmetic mean) score of students in both classes was a 77, how many students are in the second class?

A. 50
B. 75
C. 150
D. 64
E. 80



(200*75+85x)/(200+x)=77 ---> 200*75+85x=200*77+77x --> 8x=200*77-200*75 --> 8x=200(77-75)

8x=400 --> x=50
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Re: PS: Average [#permalink] New post 19 Jun 2008, 05:40
lexis wrote:
A professor gave the same exam to two classes. The 200 students in the first class scored an average (arithmetic mean) of a 75 on the exam. The students in the second class scored an average (arithmetic mean) of an 85 on the exam. If the average (arithmetic mean) score of students in both classes was a 77, how many students are in the second class?

A. 50
B. 75
C. 150
D. 64
E. 80


A = 50

200(75) + x(85) = 77(200 + x)

= 50
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Re: PS: Average [#permalink] New post 21 Jun 2008, 10:11
Expert's post
another approach for fast calculation:

\(\frac{77-75}{85-77}=\frac14=\frac{x}{200}\) --> \(x=\frac{200}{4}=50\)
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Re: PS: Average   [#permalink] 21 Jun 2008, 10:11
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