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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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A total of 45 male and female students take a math test. The average s  [#permalink]

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02 Aug 2019, 02:03
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:59) correct 11% (01:57) wrong based on 28 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 31 May 2018 Posts: 185 Location: United States Concentration: Finance, Marketing Re: A total of 45 male and female students take a math test. The average s [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7740 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A total of 45 male and female students take a math test. The average s [#permalink] ### Show Tags 04 Aug 2019, 18:58 => We can set up a 2x2 matrix using the data from the question as follows. Attachment: 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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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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