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# M21-28

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Math Expert
Joined: 02 Sep 2009
Posts: 51035

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16 Sep 2014, 00:15
3
9
00:00

Difficulty:

15% (low)

Question Stats:

88% (02:01) correct 12% (01:50) wrong based on 122 sessions

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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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Math Expert
Joined: 02 Sep 2009
Posts: 51035

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16 Sep 2014, 00:15
Official Solution:

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

Denote $$x$$ as the required number of correct answers. $$x$$ must satisfy the equation $$\frac{0.64*M*50 + x}{50M + 50} = \frac{7}{10}$$ or $$350M + 350 = 320M + 10x$$ or $$x = 3M + 35$$.

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Joined: 08 Jan 2015
Posts: 7
Location: United States (CA)
Schools: Wharton '20 (II)
GMAT 1: 730 Q47 V42
GPA: 3.63

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19 Feb 2015, 14:24
Bunuel wrote:
Official Solution:

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

Denote $$x$$ as the required number of correct answers. $$x$$ must satisfy the equation $$\frac{0.64*M*50 + x}{50M + 50} = \frac{7}{10}$$ or $$350M + 350 = 320M + 10x$$ or $$x = 3M + 35$$.

Can you split out that formula and explain why each term is in there? I don't understand how you got to $$\frac{0.64*M*50 + x}{50M + 50} = \frac{7}{10}$$
Manager
Joined: 14 Jul 2014
Posts: 93

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26 Feb 2015, 05:34
rizzy wrote:
Bunuel wrote:
Official Solution:

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

Denote $$x$$ as the required number of correct answers. $$x$$ must satisfy the equation $$\frac{0.64*M*50 + x}{50M + 50} = \frac{7}{10}$$ or $$350M + 350 = 320M + 10x$$ or $$x = 3M + 35$$.

Can you split out that formula and explain why each term is in there? I don't understand how you got to $$\frac{0.64*M*50 + x}{50M + 50} = \frac{7}{10}$$

Consider the required equation

0.64 * M * 50 + x = 7/10 * 50 ( M + 1)

0.64 * M * 50 = 50 M Questions were answered off which 64% were accurate
x = the least number of questions that the next student have to get right to bring the total of correct answers to 70%

7/10 * 50 ( M + 1) = total correct answers must be 70% . Here in (M+1) = +1 is for the next student

Hope it helps
Intern
Joined: 21 Dec 2016
Posts: 3

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05 Sep 2017, 11:24
Hi Bunuel,

I took the shortest way possible I guess but I don´t know if I´m correct at all....

Assuming M=0, the only person in doing the exam needs a 70% of correct answers.

70% of 50 = 0,7 * 50 = 35; With M=0; Answer B

Is that possible?

Math Expert
Joined: 02 Sep 2009
Posts: 51035

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14 Oct 2017, 03:17
1
Framarper wrote:
Hi Bunuel,

I took the shortest way possible I guess but I don´t know if I´m correct at all....

Assuming M=0, the only person in doing the exam needs a 70% of correct answers.

70% of 50 = 0,7 * 50 = 35; With M=0; Answer B

Is that possible?

In this case it worked but what would you do if one of the choices were 4M + 35?
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Joined: 08 Jun 2015
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Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
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11 Dec 2017, 02:18
+1 for option B. Given that there are 50 students and they answer 50 questions each. We have 50M questions. 64% of these are correct. we need to find the number of questions the 51st student needs to answer correctly to get the tally to 70%. (0.64*50M+x)/(50(M+1))=0.7. Solve and get x as 3M+35. Hence option B.
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Senior Manager
Joined: 15 Nov 2016
Posts: 282

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06 Aug 2018, 02:58
Bunuel 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

For LHS denominator why do we add 50 to 50M? Doesn't 50 M already give us the total number of questions attempted?
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Math Expert
Joined: 02 Sep 2009
Posts: 51035

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07 Aug 2018, 02:42
1
ENEM wrote:
Bunuel 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

For LHS denominator why do we add 50 to 50M? Doesn't 50 M already give us the total number of questions attempted?

M students attempted 50M questions, the next students attempts additional 50 questions, so total questions attempted 50M + 50.
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Re: M21-28 &nbs [#permalink] 07 Aug 2018, 02:42
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# M21-28

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