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A total of 45 male and female students take a math test. The average s

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A total of 45 male and female students take a math test. The average s  [#permalink]

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New post 02 Aug 2019, 02:03
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[GMAT math practice question]

A total of \(45\) male and female students take a math test. The average score for the male students is \(65\) and the average score for the female students is \(70\). Also, the combined average score for the male and female students is \(67\). How many male students took the test?

\(A. 27\)

\(B. 31\)

\(C. 33\)

\(D. 35\)

\(E. 37\)

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Re: A total of 45 male and female students take a math test. The average s  [#permalink]

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New post 02 Aug 2019, 03:58
total male and female students = 45
The average score for male students = 65
the average score for the female students = 70

let male students be x, then female = 45-x

the total score of male students = 65x
the total score of female students = (45-x)70

the combined average score for the male and female students =\(\frac{total score of male + total score of female}{total number of male +female}\)

67 = \(\frac{65x+(45-x)70}{45}\)

67*45 = 70*45-5x

5x = 45*(70-67)
5x = 45*3
x = 27
number of male students that took test = 27

A
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Re: A total of 45 male and female students take a math test. The average s  [#permalink]

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New post 04 Aug 2019, 18:58
=>

We can set up a 2x2 matrix using the data from the question as follows.

Attachment:
8.5ps.png
8.5ps.png [ 2.14 KiB | Viewed 165 times ]


The combined average is the total score divided by the total number of students. This value is
\(\frac{(65m + 70(45-m))}{45} = 67.\)

Solving for \(m\) yields
\(65m + 3150 – 70m = 3015\)

\(-5m = -135\)

\(m = 27.\)

Therefore, the answer is A.
Answer: A
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Re: A total of 45 male and female students take a math test. The average s  [#permalink]

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New post 04 Aug 2019, 20:13
This can be done by Weighted average

65(M) 70(F)
67(A)
3(70-67) 2(67-65)

M:F Ratio is 3:2

Hence \(3/5*(45) = 27\)

Hence A
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Re: A total of 45 male and female students take a math test. The average s   [#permalink] 04 Aug 2019, 20:13
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