As 64% of 50 questions are correct, Total correct answers = 0.64 x 50 x M = 32.M

Let the next student get N correct answers. And after he gives the test, the %ge of correct answers is 70%

So, Total correct answers after the next student writes the test = 0.7 x 50 x (M+1)

Equating the Total correct answers, we get

0.7 x 50 x (M+1) = 32.M + N

35.M + 35 = 32.M + N

N = 3.M + 35

Thank you for both the replies.

Gnan, I have a silly question. When M is the number of students who took the test initially then in third step why are we calculating 0.7 x 50 x (M+1)? Shouldn't M+1 be the number of students?

Thank you for clarifying.

Thank you that made it very simple

Hi All,

I'm a big fan of TESTing VALUES (the approach used in the other explanations). This question can also be solved with Algebra:

Since there are M students who averaged 64% correct on a 50 question test, we have....

M(.64)(50) = 32M points

We're going to add 1 more student; that student has to score enough points to raise the average to 70%.

X = points scored by that 1 student

Using the Average Formula, we have....

32M + X points
M + 1 students

(32M + X)/(M + 1) = .7(50)
(32M + X)/(M + 1) = 35
32M + X = 35M + 35
X = 3M + 35

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