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# The average marks of classes P, Q and R in a certain test

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Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1025
Location: India
GPA: 3.64
The average marks of classes P, Q and R in a certain test  [#permalink]

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20 Feb 2018, 11:53
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Difficulty:

55% (hard)

Question Stats:

64% (02:21) correct 36% (02:36) wrong based on 33 sessions

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The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5

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The average marks of classes P, Q and R in a certain test  [#permalink]

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20 Feb 2018, 12:31
souvonik2k wrote:
The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5

Let the students who sit in class P, Q, and R be x,y, and z

From the question stem, we get the following equations

$$\frac{62x + 71y}{x+y} = 66$$ -> $$62x + 71y = 66x + 66y$$ -> $$4x = 5y$$ -> $$y = \frac{4x}{5}$$ -> (1)

$$\frac{71y + 79z}{y+z} = 74$$ -> $$71y + 79z = 74y + 74z$$ -> $$5z = 3y$$ -> $$y = \frac{5z}{3}$$ -> (2)

From (1) and (2), we get 12x = 25z (if x=25, z=12)

Therefore, average marks of class P and R are $$\frac{62*25 + 79*12}{37}$$ = 67.5 (Option C)
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Re: The average marks of classes P, Q and R in a certain test  [#permalink]

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25 Feb 2019, 01:29
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Re: The average marks of classes P, Q and R in a certain test   [#permalink] 25 Feb 2019, 01:29
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