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# M21 #28

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27 Jun 2012, 20:39
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% ?

(A) 3M + 20
(B) 3M + 35
(C) 4M + 15
(D) 4M + 20
(E) 4M + 45

i could not understand this .. pls guide, by plugging in some values....[/quote]

the ans is B..
I solved it by taking M as 1 . M scored 64% that is he scored 32 out of 50 to get a total of 70% after another student appear for exam he/she should score 38 ( (32 + x)/100 * 100 = 70 ; solving for x, we get 38 ). Now eliminating other options we get B
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02 Jul 2012, 10:36
im not sure why every body is making such an easy problem sound so complicated
this can be made simpler by substitution method

the test contains 50 questions and currently M students keep it at 64% so i dont want to multiply some no withh 64 so i make the no of students=2
so total questions 100
no of correct answers in them =64%*100=64
one more student comes in so no of questions=150 in total
70% of 150=105
=> 105-64=41 questions have to be answered correctly by other student

we assumed m=2 i.e no if students

so by substitution in answer choices 3M+35 (option B ) only holds true this might seem long but a lot easier to do

hope it helps afterall we want to get answer the fastest way not the ideal way
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27 Jun 2013, 05:23
what is the least number of questions ----> (one of the answers given as options) that the next student ----> (1 student in place of M).
We know that 64% of 50 is 32 and 70% of 50 is 35. It means that the least number of questions must be greater than or equal to 35 questions to get right to bring the total of correct answers to 70%.

(A) 3M + 20 = 3*1+20 = 23--> which is less than 35
(B) 3M + 35 = 3*1+35=38 --> hummm, looks fine.
(C) 4M + 15 = 4*1+15 =19--> No way
(D) 4M + 20 = 4*1+20 =21--> No way
(E) 4M + 45 = 4*1+ 45=49--> No need of these many... ha ha ha.. so answer is B --> 3M+35
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27 Jun 2013, 19:31
arjtryarjtry wrote:
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% ?

(A) 3M + 20
(B) 3M + 35
(C) 4M + 15
(D) 4M + 20
(E) 4M + 45

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

i could not understand this .. pls guide, by plugging in some values....

Concept - Averages
We have M students that got 64% Correct answers ( out of 50), hence number of correct answers = M * (64% * 50) = 32M
We need 'x' correct answers more for the next student to get the average upto 70% = x (correct answers)

Sum of weighted Averages = (32M + x ) / (M+1 ) = 70% of 50 = 35

Solve for x => x = 3M + 35
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01 Jul 2013, 13:40
This can be done using weighted averages:

70% of 50 = 35 (Reqd avg of all the students)
64% of 50 = 32 (Avg of M students)

Let A be the correct number of questions that the last student has to answer

Now,

35 = [M/(M+1)]*32 + [1/(M+1)]*A

-- Multiply both sides by (M+1)

35M + 35 = 32M +A

Thus, A = 3M + 35

Ans is B.
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13 Jun 2014, 02:06
Solution:

M students each attained 50 Qs and performed correct with 64% , so no of correct questions are - 50 * M * 64/100

when next student comes,

M+1 students each attained 50 Qs and performed correct with 70% , so no of correct questions are - 50 * M * 70/100

Therefore, the difference is the no. of correct questions the last student performed...

i.e. 3M + 35 (Ans)...
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13 Jun 2014, 06:23
Really great explanation.

jallenmorris wrote:
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
Re: did nt understand   [#permalink] 13 Jun 2014, 06:23

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# M21 #28

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