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# Value of z and y are?

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Manager
Joined: 24 Apr 2013
Posts: 52

Kudos [?]: 11 [0], given: 76

Schools: Duke '16
Value of z and y are? [#permalink]

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30 Apr 2013, 14:44
The integers y and z are positive. A group of y juniors and z seniors took a test. The average (arithmetic mean) score of the juniors was 75, the average score of the seniors was 87, and the average score of all the juniors and seniors combined was 84.

In the table below, pick two numbers that are consistent with the information that is given. In the first column, select the row that shows the value of y, and in the second column, select the row that shows the value of z.

Kudos [?]: 11 [0], given: 76

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2375 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Value of z and y are? [#permalink]

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30 Apr 2013, 15:08
1
KUDOS
You have not posted the table but here is the solution anyway

$$\frac{75y+87z}{y+z}=84$$, this is totScores/ totNumbers.Rewrite it:

$$75y+87z=84y+84z$$
$$3z=9y$$ every pair that respect this is valid

z=3 y=1
$$\frac{75+87*3}{4}=84$$
z=36 y=12
$$\frac{75*12+87*36}{40}=84$$

with the table: Value of y Value of z

18<-y
27
36
42
54<-z
72

Hope it's clear, let me know
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Kudos [?]: 2375 [1], given: 219

Manager
Joined: 24 Apr 2013
Posts: 52

Kudos [?]: 11 [0], given: 76

Schools: Duke '16
Re: Value of z and y are? [#permalink]

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30 Apr 2013, 15:41
sorry about that: question can be found here http://lomath.net/gmat/2part/q11/2pq11.html

I sort of understand. I would like to know why you did 75y+87Z/z+y as I did divided by 2 with the reasoning that the mean is a sum of numbers divided by the number of numbers

Kudos [?]: 11 [0], given: 76

Re: Value of z and y are?   [#permalink] 30 Apr 2013, 15:41
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# Value of z and y are?

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