Really great explanation.
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%.
arjtryarjtry wrote:
i could not understand this .. pls guide, by plugging in some values....
After M students took the test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70% ?
Club - m21#28
* 3M + 20
* 3M + 35
* 4M + 15
* 4M + 20
* 4M + 45