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Intern  Joined: 21 Feb 2008
Posts: 37
Location: United States
Concentration: Marketing, Nonprofit
After M students took a test, there was a total of 64% of  [#permalink]

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9 00:00

Difficulty:   25% (medium)

Question Stats: 78% (02:22) correct 22% (02:21) wrong based on 114 sessions

### HideShow timer Statistics After M students took a 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
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Posts: 28
Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39 GPA: 3.62
WE: Engineering (Energy and Utilities)

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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
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rakp wrote:
After M students took a 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

It is a weighted average question!
Out of 50M questions, 64% are correct. Out of 50 questions, you need x% to be correct so that the total % of correct answers is 70%.

w1/w2 = 50M/50 = (x -70)/(70 - 64)
6M = x - 70
x% = (6M + 70)%

Therefore, out of 50 questions, (6M + 70)% i.e. (6M + 70)/100 * 50 = (3M + 35) questions must be correct.

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Karishma
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Intern  Joined: 21 Feb 2008
Posts: 37
Location: United States
Concentration: Marketing, Nonprofit
Re: After M students took a test, there was a total of 64% of  [#permalink]

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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.
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Re: After M students took a test, there was a total of 64% of  [#permalink]

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1
1
rakp wrote:
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.

I think that equation is equal to the number of questions that the new student and the old students got correct.

70% = (old correct answers + new correct answers)/(old number of questions + new questions)

Old Correct Answers = 64% * (50M) where 50M is the total number of old questions

New Correct Answers = x, the variable we are trying to find

Old Number of Questions = 50M

New Number of Questions = 50

So with that:

70% = (32M + x)/(50M + 50)

Then you can solve for x.
Intern  Joined: 21 Feb 2008
Posts: 37
Location: United States
Concentration: Marketing, Nonprofit
Re: After M students took a test, there was a total of 64% of  [#permalink]

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Thank you that made it very simple Retired Moderator B
Joined: 05 Jul 2006
Posts: 1657
Re: After M students took a test, there was a total of 64% of  [#permalink]

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rakp wrote:
After M students took a 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

let m = 100 thus answer choices becomes a) 320 b) 335 c) 415 d)20 in terms of numbers

Now 100 students answered right question = 64/100* (5000) = 50*64 = 3,200 questions out of 5000

now an extra student is to be added to bring the % of correct questions to 70% of all answered. all answered including the new student = 5, 050

thus

x/5050 = 7/10 thus x = 3,535 question right so we need to increase number of right questions to 3,535 from 3200 that is by answering 335 right questions ... option B
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: After M students took a test, there was a total of 64% of  [#permalink]

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1
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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www.empowergmat.com/ Re: After M students took a test, there was a total of 64% of   [#permalink] 27 Feb 2018, 11:17
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