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Torry has submitted 2/5 of his homework assignments, and he received

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Bunuel
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Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   19 Dec 2019, 04:31
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Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 90 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?

A. 15%
B. 20%
C. 25%
D. 33 1/3%
E. 40%
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D
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   19 Dec 2019, 11:15
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Kudos
total assignments = 5
so for 2 assignments he has received = 150 points
and for all wishes ; 90*5 ; 450 points
he is short of = 300 points
i.e avg score per assigment required = 100 points
i.e 100-75/75 = 25/75 = 1/3 ; 33 1/3%
IMO D


Bunuel wrote:
Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 90 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?

A. 15%
B. 20%
C. 25%
D. 33 1/3%
E. 40%
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   19 Dec 2019, 17:29
I would go for D.
Total assignment=5
Average in first 2= 75 i.e. 150 total
Expected average in 5= 90 i.e. 450 total.
So, 300 (450-150) needed from remaining 3. i,.e 100 points each.
so, 25 more points needed. Thus, 25/75=33.33% more points needed on an average.
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   20 Dec 2019, 10:53
use allegation method

the given ratio of higher marks : 75 = 3:2 (total was 5)
average = 90
hence
75 higher
\ /
90
/ \
2 3

\(\frac{higher -90}{ 90-75}= 2/3\)
solve for higher
and higher = 100
now percent greater is
\(\frac{100-75}{75} *100\)

which is 33.33
or \(33\frac{1}{3}\)
hence D
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   20 Dec 2019, 12:16
Here, Focused wording " received" and "wishes to receive"

Let total number of assignment = 5

Torry has received total grade = 75 x 2 = 150

He wishes to receive total grade = 90 x 5 = 450

Remaining grade = 450 - 150 = 300 and Remaining grade average = 300/3 = 100

Grade average to be achieved = 100 - 75 =25

Answer = 25/75 = 33.33 %
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink] New post   26 Dec 2019, 21:29
Expert Reply
Bunuel wrote:
Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 90 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?

A. 15%
B. 20%
C. 25%
D. 33 1/3%
E. 40%


We can create the equation:

(2/5)*75 + (3/5)*N = 90

30 + 3N/5 = 90

3N/5 = 60

3N = 300

N = 100

So, the average grade for Torry’s remaining assignments must be 100. As a percentage, the remaining assignments must be:

(100 - 75)/75 x 100 = 25/75 x 100 = 1/3 x 100 = 33 ⅓% greater than the previous assignments.

Answer: D
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Re: Torry has submitted 2/5 of his homework assignments, and he received [#permalink]
26 Dec 2019, 21:29
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