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Algebra

by prernamalhotra » Mon Jun 30, 2014 4:07 am
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x % of the black-and-white films and all of the color films, what fraction of the selected films are in color?

1) 1/130
2) 1/5
3) 3/13
4) 10/13
5) 30/31

[spoiler]I am getting 3/13 by plugging in x =2, y=3, therefore 18/60+18, 18/78 =3/13, but the right answer is (5)[/spoiler]
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by GMATinsight » Mon Jun 30, 2014 4:20 am
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x % of the black-and-white films and all of the color films, what fraction of the selected films are in color?

1) 1/130
2) 1/5
3) 3/13
4) 10/13
5) 30/31
Total Selected films = [(y/x)/100]*20x + 6y

Total Selected Color Films = 6y

Required %age = 6y*100 / {[(y/x)/100]*20x + 6y)} = [spoiler]30/31 Option E[/spoiler]



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by GMATinsight » Mon Jun 30, 2014 4:24 am
The Alternate approach is here


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by GMATinsight » Mon Jun 30, 2014 4:34 am
I am getting 3/13 by plugging in x =2, y=3, therefore 18/60+18, 18/78 =3/13, but the right answer is (5)
Hi Prerna,

Your mistake is in calculation of (y/x)% of total films selected

It should be [(3/2)/100]*20*2 = 3/5 = 0.6 which you, by mistake, have taken 60

If you correct it then the calculation will be

18/(0.6 + 18) = 18/18.6 = 180/186 = 30/31 ANSWER
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by GMATGuruNY » Mon Jun 30, 2014 4:49 am
prernamalhotra wrote:A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x % of the black-and-white films and all of the color films, what fraction of the selected films are in color?

1) 1/130
2) 1/5
3) 3/13
4) 10/13
5) 30/31
Let y=100 and x=1, with the result that (y/x)% = (100/1)% = 100%.
Implication:
Since (y/x)% of the black-and-white films are selected, 100% of the black-and-white films are selected.
Since 100% of the color films are also selected, ALL OF THE FILMS ARE SELECTED.

Number of black-and-white films = 20x = 20*1 = 20.
Number of color films = 6y = 6*100 = 600.
color/total = 600/620 = 30/31.

The correct answer is E.
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