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

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A professor gave the same exam to two classes. The 200 [#permalink]

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19 Jun 2008, 05:03
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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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Director
Joined: 14 Aug 2007
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19 Jun 2008, 05:44
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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CEO
Joined: 29 Mar 2007
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19 Jun 2008, 05:57
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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Senior Manager
Joined: 07 Feb 2008
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19 Jun 2008, 06:40
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

Kudos [?]: 186 [0], given: 1

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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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21 Jun 2008, 11:11
another approach for fast calculation:

$$\frac{77-75}{85-77}=\frac14=\frac{x}{200}$$ --> $$x=\frac{200}{4}=50$$
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Kudos [?]: 4661 [0], given: 360

Re: PS: Average   [#permalink] 21 Jun 2008, 11:11
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