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Re: There are 32 students in Jamie’s eighth-grade class. Each st [#permalink]
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sandy wrote:
There are 32 students in Jamie’s eighth-grade class. Each student took a 50-point test; the class average (arithmetic mean) was 82% correct. The teacher has assigned one 4-point, extra-credit question. How many students will need to answer the extra-credit question correctly in order to bring the class average to 86% correct?

A. 15
B. 16
C. 17
D. All of the students
E. It will not be possible for the class to reach an average of 86% correct.


We can create the equation:

(0.82(50)(32) + 4x)/32 = 0.86(50)

0.82(50)(32)/32 + 4x/32 = 0.86(50)

41 + x/8 = 43

x/8 = 2

x = 16

Alternate Solution:

Each test point is worth 2%. Thus, the extra credit question is worth 4 points, or 8%. If all 32 students answered it correctly, then the class average would increase by 8%. Since we want to increase the class average by only 4%, then only half of the students (i.e., 16 students) need to answer it correctly.


Answer: B
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Re: There are 32 students in Jamie’s eighth-grade class. Each st [#permalink]
sandy wrote:
Explanation

If the class average is 82% on a 50-point test, the average score was 41 points out of 50.

Use the Average Pie to find the sum of the class’s scores: (41)(32) = 1,312. To reach a class average of 86%, each student will need to average 43 points out of 50 points. Use the Average Pie to find the desired sum of the class’s scores: (43)(32) = 1,376. The difference is 1,376 − 1,312 = 64, so the class needs to make up 64 points;\(\frac{64}{4} =16\), so 16 students need to answer the extra credit question correctly. The answer is B.

Alternatively, notice that the class’s average needs to increase by 4%, or 2 points on average for a 50-question test. But the extra credit is
worth 4 points, so to average half of a 4-point increase, only half the students (16) need to get the extra credit correct.

I was confused because i thought some will get 1 out of 4, some 2 out of 4, some 3 and some 4 out of 4.
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Re: There are 32 students in Jamies eighth-grade class. Each st [#permalink]
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