bdennis wrote:

Hi, I need some help understanding why my reasoning is wrong for this question from Princeton Review Math Workout for the GMAT 2nd edition, p. 268, #10:

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%

Correct answer: d. 33 1/3%

My faulty solution:

First two HW assignments: x1 + x2 = 2*0.75

Wish five HW assignments: (x1 + x2) + (x3 + x4 + x5) = 5*0.9

2*0.75 + (x3 + x4 + x5) = 5*0.9

x3 + X4 + x5 = 5*0.9 - 2*0.75 = 3

(x3 + x4 + x5)/3 = 1

Therefore, the average of assignments x3, x4, x5 must be 100% and the percent increase from 75% to 100% is 25%.

Thanks in advance for your help.

your solution is correct till the last step.

Generally, to find by what percent x is greater than y, we use the following formula:

((x-y)/y)*100--------------------------------1)

now in this we have to find by what percent average of the remaining three tests is greater than the average of the first two test.

so here x=100 and y=75

substituting these values of x and y in the equation 1) we have

(25/75)*100 = 33(1/3)%