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Bunuel
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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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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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Bunuel
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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