The answer is 3M + 35.

We know that M students took the test and there is a total of 64% of the answers correct. This means that 64% of 50 questions were right, on average. We know it's on average because they tell us the total of correct answers. So if you add up all correct answers for M test takers and divde that by the number of test takers * 50, it gives you 64%.

64% of 50 is 32 questions correct on average. So now, we need to figure out how many questions would be correct on 1 test to get 70% So 70% of 50 questions is 35 correct answers. In order for the next test taker to bring the total correct to 70%, the test taker must get 35 questions correct AND make up the difference of the other test takers. By difference, I mean these other test takers got 32 questions right, and to get 70% they should have gotten 35 correct. Each prior test taker is 3 short. So this next one must 35 correct for their own 70% score plus 3 questions to make up the difference.

If you had 1 prior test taker, out of 50 questions the prior taker got 32 right, for a score of 64%. The next one needs to get 35 questions right for their own 70%, but if you added both together, you'd have 35 + 32 correct for 67 out of 100, and that's just 67%. So, the second test taker must get 3 extra questiosn correct so that the total is 70 out of 100. so since there was 1 test taker in this example, M = 1 here. So the answer is 3M + 35.

3 questions per prior test taker to make up the average + 35 questions correct to make sure this test taker gets 70% too!

Hope this explanation is helpful. You might also see a variation of this question like this:

18 students took a test with 50 questions. The 18 students averaged 64% correct answers. If 3 more students take the exam, is it possible for these 3 students to raise the average to 70% correct answers?

You'd figure this out by realizing how many correct answers the first 18 students were short to get 70%. Because we're using the same numbers, we know they average 32 out of 50. So they were each on average 3 questions short. If 18 students were 3 questions short, that's a total of 48 questions. The question tells us that we have 3 more students to take the exam. Each of these new students needs to get 35 (for 70%) correct + some to make up the difference. Since there are 15 questions that are not required to get a 70%, these are questions that can be answered correctly to increase the average of all students. If there are 15 questions that can help to raise the average and there are 3 students remaining to take the exam, then there are 45 questions left that can be used to raise the average of the others. We already figured out that we need 48 questions correct in addition to the questions answered to get the 70% average. There are not enough coming test takers to raise the average to 70% from 64%.


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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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my quick approach:
64% of 50 by M students = 32M
70% of 50 by (M+1) students = 35M + 35

so the the least number of questions that the next student has to answer correctly: 35M + 35 - 32M = 3M + 35
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GT

Answer is (B) 3M+35

3M to make up for the 6% (=70-64) of others and 35 to get 70% on the 50 question test

I guess my question really is this---if 10 students had taken the test, isn't this implying that the next student has to get a 65/50 (3M+35)? Which wouldn't that be impossible?

I'm not sure that I"m reading this question correctly, but it seems as if it is saying that 1 student has to make up the difference?

I am too stupid for abstract solutions, so facing such questions, I always use real-life example. In that case I set M=2, and calculated the number of correct solutions, and then in A-E I found a variant that will match my number.

Sol:

\frac{x-70}{70-64}=\frac{50M}{50}

\frac{x-70}{6}=M

x=6M+70

x is percent. Number would be,

\frac{(6M+70)*50}{100}

3M+35

Ans: "B"
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A simple non-technical approach...

We know that 64% = 32 correct answers

70% = 35 correct answers

So even if there was only one student who got 64%...the other student will need to get 76% (38 correct) to bring up the average to 70% (35 right answers).

If we look at the answer choices -- we can right away eliminate the wrong answers -- by just substituting (M= 1)...

Approached using GMAT Tiger's method. Quick and effective. Kudos to Allen for his thoroughness though.

Cheers,
Der alte Fritz.
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+1 Kudos me - I'm half Irish, half Prussian.

Well, its very simple..
64% of 50 questions = 32
70% of 50 questions = 35.

to make the total avg 70% the next student must score 70% for himself + cover up the lackings of right answers to make the 'M' previous students' avg 70% also.
as each previous M# of students lack by 3 questions to avg. 70%, the new student must score 3*M extra right answers besides his 70%(35 right answers).

thus the answer is 3*M + 35

lets rephrase the question.

If M students get an average score of 64% out of 50, that is 32 marks. Then how much does the next student need to score to increase the average marks to 70% of 50, that is 35.

so the equation can be put as

32*M + x = 35*(M+1),

where 32*m is the total score of m students and x is the score needed by the next student.
35*(m+1) is the total score by M+1 students.


32*M + x = 32M + 3M + 35

we can see the answer now, its B.