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.32%
D.37%
E.43%

bhumika.k.shah wrote: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.32%
D.37%
E.43%

Say there are 3 judges and one gave 70/110 to Darlene
To average 90/110 she needs a total of 270/110
That is an average of 200/220 or 100/110 from the rest of the judges

score increase = 30/70*100 = 43%

how much time did this take you to solve???

ajith wrote:

bhumika.k.shah wrote: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.32%
D.37%
E.43%

Say there are 3 judges and one gave 70/110 to Darlene
To average 90/110 she needs a total of 270/110
That is an average of 200/220 or 100/110 from the rest of the judges

score increase = 30/70*100 = 43%

bhumika.k.shah wrote:how much time did this take you to solve???

Well I think I can do it in less than 2 minutes but, it is a hunch feeling.

it becomes a whole let easier if you put it in an equation and simply the values

1/3rd gave 70 out of 110. what should 2/3 give to make it 90/110 can be written as follows:

(1/3)(70/110) + (2/3)x = 90/110

--> (1/3)(7/11) + (2/3)x = 9/11

--> (2/3) x = 9/11 - 7/33

--> (2/3)x = (27-7)/33 = 20/33

--> x= 60/66 = 10/11

Percentage Increase = [(10/11 - 7/11)/ 7/11] * 100% = 3/11 * 11/7 * 100 = 3/7 * 100 = 42. ... ~ 43%

Though the explanation looks long, I assure you that it will take you barely more than a minute.

Remember to memorize your fraction -> decimal conversions upto 1/20. This will save you a lot of time on the test.

Though the explanation looks long, I assure you that it will take you barely more than a minute.

I agree.

i am glad i understood a different approach!

[quote="sars72"

Remember to memorize your fraction -> decimal conversions upto 1/20. This will save you a lot of time on the test.[/quote]

hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

i completed this the same way that sars72 did... it seems confusing at first, but when you break it down and realize it's all just regular / fractional multiplication it's not that bad...

Maybe this is the wrong way to do the problem, but this is how I went about it...

I ignored the fact that we're dealing with 70/110 and 90/110 and just took it as 70 and 90.

Determined that for her to get a 90 average her total should be 3 * 90 = 270

We've already been told that 1 of her managers gave her a 70: 270-70 = 200
2 of her managers are left and she needs to average a 100 on both to get a 90.

Percent Increase = (100-70)/70 = 3/7 = ~43%

Thoughts?

aakar wrote:Maybe this is the wrong way to do the problem, but this is how I went about it...

I ignored the fact that we're dealing with 70/110 and 90/110 and just took it as 70 and 90.

Determined that for her to get a 90 average her total should be 3 * 90 = 270

We've already been told that 1 of her managers gave her a 70: 270-70 = 200
2 of her managers are left and she needs to average a 100 on both to get a 90.

Percent Increase = (100-70)/70 = 3/7 = ~43%

Thoughts?

It's not wrong at all!

That's the freedom we can use when we just have averages (e.g 70 & 90) , fractions in variables(e.g 1/3 & 2/3) and percentages .

i like

simple to understand!

quote="aakar"]Maybe this is the wrong way to do the problem, but this is how I went about it...

I ignored the fact that we're dealing with 70/110 and 90/110 and just took it as 70 and 90.

Determined that for her to get a 90 average her total should be 3 * 90 = 270

We've already been told that 1 of her managers gave her a 70: 270-70 = 200
2 of her managers are left and she needs to average a 100 on both to get a 90.

Percent Increase = (100-70)/70 = 3/7 = ~43%

Thoughts?[/quote]

I found a new way of doing this problem.

Given 70 of 110 evaluation at 1/3 observations so -- 70*x*110/3*100 -- 77x/3

Desired 90 of 110 evaluations at 2/3 observations so -- 90*2x*100/3*100 -- 191x/3

what % does the average score increase on her 2/3 oberservations

So -- 191x/3 - 77x/3 = 43.3x (remember we have already divided both the equations by 100 so the answer now is directly 43.3%)

agree with all the above posts, but i think allegation is the easiest way:

as we need to calculate the increase( take 70 as the base)




=> (x-20)/20 = 1/2 => x = 30

bhumika.k.shah wrote: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.32%
D.37%
E.43%

Let the number of supervisors = 3.
The sum of the 3 scores = number*average = 3*90 = 270.
The number of supervisors who gave a score of 70 = (1/3)3 = 1.
The sum of the scores of the other 2 supervisors = 270-70 = 200.
Average score from these 2 supervisors = sum/number = 200/2 = 100.
Percent increase from 70 to 100 = Difference/Original * 100 = 30/70 * 100 ≈ 43.

The correct answer is E.

Hi guys, I am new to GMAT but confused on this one.

I read the question as:

She has 70/110 (63%) so far, and needs 100/110 (91%) from the remaining 2/3 to hit her desired average of 90/110.

91-63 = 28?

Given everyone interpreted the q differently, i am obviously wrong. is there some wording that i have not picked up on?