There are 32 students in Jamie’s eighth-grade class. Each student took

Question

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. 18
E. 19

A. 15
B. 16
C. 17
D. 18
E. 19

chandan1988 · Accepted Answer

Soln::
class average was 82% correct 
i.e. 82% of 50 = 41 marks scored on average by students

(sum of the Student's score)/ no of students = 41

=> sum of student's score = (41*32)
 = 1312

If the average is to be increased to 86% then marks to be obtained is (86% of 50= 43)

Let the number of students answered extra credit points be X

SO, (1312+4X)/32= 43

X= 16 Ans
 B

pushpitkc · Answer

For a 50-point test, if the class average is 82%, the average score must have been 41.
Since the new average must increase to 86%, the new average score must be 43.

So, in order to improve the overall average by 2, 50% of the class must get the 4-point(extra-credit question) correct.

Therefore,  \frac{50}{100}*32 =   16(Option B)  students need to get the question correctly(for average to become 86%)

zishu912 · Answer

for the 50 point test 82 % is 41 point so the total points of 32 students is = 41 * 32 = 1312
86 % of 50 = 43 so the new total will be = 32 * 43 = 1376

The difference = 1376 - 1312 = 64

so 16 students need to answer the extra credit question correctly (16 * 4)

Hence B is the correct choice

ScottTargetTestPrep · Answer

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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