Because her test turned out to be more difficult than she intended it

Question

Because her test turned out to be more difficult than she intended it to be, a teacher decided to adjust the grades by deducting only half the number of points a student missed. For example, if a student missed 10 points, she received a 95 instead of a 90. Before the grades were adjusted the class average was A. What was the average after the adjustment?

A. \(50 + \frac{A}{2}\)

B. \(\frac{1}{2}\) * \((100 - A)\)

C. \(100 -\) \(\frac{A}{2}\)

D. \(\frac{50 + A}{2}\)

E. \(A + 25\)

A.  50 + \frac{A}{2}

B.  \frac{1}{2}  *  (100 - A)

C.  100 -   \frac{A}{2}

D.  \frac{50 + A}{2}

E.  A + 25

RohitGoyal1123 · Accepted Answer

The question tells you that 100 is the maximum score (from the example with 90 and 95). So you know that A=100-W where W is the number they got wrong.

Under the new system A' would be 100- \frac{W}{2} . Right?

So Rearranging the first equation for W gives W=100-A and substituting gives:

A'=100-\frac{(100-A)}{2}=100-50+\frac{A}{2}=50+\frac{A}{2}

Hence  A

AkshdeepS · Answer

Question is simply asking which answer choice gives 95 marks when we use A equals 90.

Only answer choice A gives this .

50 + 90/2

= 95 (A)

JeffTargetTestPrep · Answer

Since the average is A, we see that, on average, each student misses (100 - A) points. Since the teacher decided to deduct only half the number of points a student missed, on average, she deducted (100 - A)/2 points from each student. Therefore, the new average is:

100 - (100 - A)/2 = 100 - 100/2 + A/2 = 50 + A/2

Answer: A

MathRevolution · Answer

The total is 100 and the Average is 100.

Students miss (100-A)

Now as deduction is halved, new miss point is  \frac{(100 - A)}{2}

New Average: 100 -  \frac{100}{ 2} + \frac{A}{2}

=> 50 +  \frac{A}{2}

Answer A

bumpbot · Answer

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Because her test turned out to be more difficult than she intended it

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