Problem Solving

Darlene averaged a score of 70 out of 110 on evaluations from 1/3 of her supervisors. If Darlene wishes to average a score of 90 out of 110 on all of her evaluations, by approximately what percent must her average score increase on the remaining 2/3 of the evaluations?


a) 20%
b) 28%
c) 30%
d) 43%
e) 50%


I keep getting 28% as the answer but that is not correct according to the test.

I think the answer should be E.

He originally scored around 63%.

He must average approx... 87% on the other 2 evaluations to bring his overall average score to 90/110.

so, his original score must increase by about 50%.

what's the OA.

Question is from Princeton Review practice test. OA is 43%. I think I figured our how they get this. I was making a stupid mistake. Here is how to get the correct answer:


if average of 1/3 is 70 and we need the average for all scores to be 90 we can use the equation 70+2x/3=90 and solve for x to get the average score needed by the last 2/3 of the supervisors? Then its just a matter of finding the percentage increase between these scores. I get x=100, thus percentage increase =100-70/70=43%

I screwed up because I took 90-70/70 which equals 28%.

ok in easy words is:
70 from one supervisor; we dont' know the results from anothers 2 supervisors... but we only know that the average has to be 90...so

[(70+x+x)/3]=90
then
x=200/2 --------100

now we know that the results from the anothers 2 supervisors are 100

so finding the increment:
70(1+?)=100
x=30/70...............=43

Guys,

Here's how I came to the answer:

70/110 from 1/3 of evaluations.
Objective is to get an average score of 90/110 from all (3/3) evaluations.

Lets assume she had 3 evaluations. And lets assume that she averaged a score of 90/110 over all 3 of her evaluations. This would give her a total of ((90*3)/(110*3)) 270/330.

So 270/330 is the target.
We know she has got 70/110 already.

70/110 + x/110 + x/110 = 270/330

From this we can easily see that x must be 100 (which over the remaining evaluations will provided the additional 200 score to get to the target of 270/330).

So 70/110 + 100/110 + 100/110 = 270/330, which provides an average of 90/110.

This means that in each of her next 2 evaluations she needs to get an additional 30 points on top of the 70 which she scored in her 1st evaluation. To calculate this as a percentage: 30/70 = 43%

P.S. Another habit I am adopting is to simplify the fractions ... so when doing the calculations ... I would use 7/11 instead of 70/110. Or use 9/11 instead of 90/110. Or 27/33 instead of 270/330. When working with smaller numbers it makes it easier (for me anyway !).

Hope this helps.

By the way ... what level of difficulty is this question classified as:
Low, medium, or High ?

i'd say low to medium?

Bschool08 wrote:i'd say low to medium?

Thanks .. sounds about right !