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A committee is reviewing a total of 20x black-and-white film

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A committee is reviewing a total of 20x black-and-white film [#permalink]

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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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)
[Reveal] Spoiler: OA

Last edited by hazelnut on 15 Oct 2017, 00:48, edited 2 times in total.
Renamed the topic and edited the question.
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 07 Jul 2013, 08:50
kingflo wrote:
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects % of the black-and-white films and all of the color films, what fraction of the selected films are in color?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31


Had a "not so good" time with this question! ;-)

Dude are you sure you are not missing anything in the highlighted portion?
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 07 Jul 2013, 09:07
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kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


Say x=y=10. In this case we would have:

20x=200 black-and-white films;
6y=60 color films.

y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.

Color films thus compose 60/62=30/31 of the selected films.

Answer: E.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention tot he rule #3. Thank you.
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 07 Jul 2013, 09:37
Vips0000 wrote:
kingflo wrote:
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects % of the black-and-white films and all of the color films, what fraction of the selected films are in color?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31


Had a "not so good" time with this question! ;-)

Dude are you sure you are not missing anything in the highlighted portion?


Sorry Vips0000, I had already hit "submit" when I realized that the fraction had not copied correctly. And then the topic was locked.
But thanks to Bunuel the confusion did not last too long ;-)
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 07 Jul 2013, 09:49
Bunuel wrote:
kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


Say x=y=10. In this case we would have:

20x=200 black-and-white films;
6y=60 color films.

y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.

Color films thus compose 60/62=30/31 of the selected films.

Answer: E.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention tot he rule #3. Thank you.


Hi Bunuel, is there an algebraic way for doing this?
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 07 Jul 2013, 10:01
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Spaniard wrote:
Bunuel wrote:
Say x=y=10. In this case we would have:
20x=200 black-and-white films;
6y=60 color films.
y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose 60/62=30/31 of the selected films.
Answer: E.
Hope it's clear.
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention tot he rule #3. Thank you.

Hi Bunuel, is there an algebraic way for doing this?


Sure there is..

Total Selected films = 20x* (y/x)% + 6y = 20y/100 +6y =31y/5
Color films = 6y

Fraction required in question = 6y / (31y/5) = 30/31

Ans E it is..
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 22 Oct 2013, 09:12
Bunuel wrote:
kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


Say x=y=10. In this case we would have:

20x=200 black-and-white films;
6y=60 color films.

y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.

Color films thus compose 60/62=30/31 of the selected films.

Answer: E.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention tot he rule #3. Thank you.


I thought 10%/10%=100%, also, what if x and y don't equal each other, like say x is 10,000 and y is 3.

let's say X=30 here, and y =4; you get 600 B&W films, and 24 color. y/x%=~13.333%, so 13.333% of 600 B&W films = 80 B&W and 24 color. You can't solve this problem for sure, you could get any number you wanted by just changing what x and y equal, there's two variables here. You could come up with values that gave you any of the answers.
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 22 Oct 2013, 09:19
AccipiterQ wrote:
Bunuel wrote:
kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


Say x=y=10. In this case we would have:

20x=200 black-and-white films;
6y=60 color films.

y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.

Color films thus compose 60/62=30/31 of the selected films.

Answer: E.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention tot he rule #3. Thank you.


I thought 10%/10%=100%, also, what if x and y don't equal each other, like say x is 10,000 and y is 3.


If x=y, then x/y=1. How else?

Next, I chose smart numbers which are easy to plug. You can try and proceed with x=10,000 and y=3.
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 10 Jan 2014, 09:04
kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


Use smart numbers for this one

y=100
x=2

Then Color films 600
Black and White are 20

Color/Total = 600/620=30/31

E
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 02 Sep 2014, 06:34
i got different results by plugging x=20 , y=10

b&w= 400
colored= 60

selected B&W= 10/20 x 400=200

fraction of colored films= 60/260=3/13

please advise what did i do wrong
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 02 Sep 2014, 07:02
Kholoud wrote:
i got different results by plugging x=20 , y=10

b&w= 400
colored= 60

selected B&W= 10/20 x 400=200

fraction of colored films= 60/260=3/13

please advise what did i do wrong


It's y/x percent not y/x.

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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31


If x=20 and y=10. Then:

20x=400 black-and-white films;
6y=60 color films.

y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.

Color films thus compose 60/62=30/31 of the selected films.

Answer: E.
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 02 Sep 2014, 15:22
Bunuel: what's wrong with the following? This is where I seem to go wrong (y/x%) = (y/x/100) which is 100y/x?
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 31 Mar 2016, 17:06
Attached is a visual that should help.
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Screen Shot 2016-03-31 at 6.06.03 PM.png
Screen Shot 2016-03-31 at 6.06.03 PM.png [ 121.6 KiB | Viewed 2698 times ]


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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 01 Jul 2016, 11:12
Misinterpreted the question and went for C because I thought of all the possible films. smh
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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So you can simply pick any crazy numbers you want for x and y?
1) why does this work
2) how would you recognize that this works?
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Re: A committee is reviewing a total of 20x black-and-white film [#permalink]

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New post 21 May 2017, 19:01
kingflo 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?

A. 1/130
B. 1/5
C. 3/13
D. 10/13
E. 30/31

Had a "not so good" time with this question! ;-)


There are many ways to tackle this problem, but I think mine achieves relative speed and reliability.

First create a table with all movies in column 1, selected movies in column 2, B/W in row 1, and color in row 2.

Then fill in the grid. The tricky part here is that the total number of black and white films is equal to y/x PERCENT of 20x, so we need to write down the following algebraic translation: y/x*1/100*20x. The division by 100 turns y/x into a percent instead of a fraction or ratio.

Then we need to solve for the share of color films of total selected films: 6y/(6y + y/x*1/100*20x)

This part reduces to 6y/(6y+y/5), then to 6y/(31y/5, then to 30y/31y or 30/31.
Re: A committee is reviewing a total of 20x black-and-white film   [#permalink] 21 May 2017, 19:01
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