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

Question

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! ;-)

Bunuel · Accepted Answer

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.

Vips0000 · Answer

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..

Vips0000 · Answer

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

kingflo · Answer

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 ;-)

Spaniard · Answer

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

AccipiterQ · Answer

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.

Bunuel · Answer

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.

jlgdr · Answer

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

Kholoud · Answer

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

Bunuel · Answer

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 % 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! ;-)

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.

bankerboy30 · Answer

Bunuel: what's wrong with the following? This is where I seem to go wrong (y/x%) = (y/x/100) which is 100y/x?

Bunuel · Answer

20% is 20/100, the same way  \frac{x}{y}%  is  \frac{(\frac{x}{y})}{100} = \frac{x}{100y} .

mcelroytutoring · Answer

Attached is a visual that should help.

alpham · Answer

Misinterpreted the question and went for C because I thought of all the possible films. smh

mromrell · Answer

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?

mbaapp1234 · Answer

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.

kosio01 · Answer

Rarely use algebraic approach with these questions but I decided to do it here and it worked out beautifully.

So we know that total B&W=20x and total C=6y. 
Then selected B&W is y/x% of 20x or y/x*1/100=y/100x of 20x, i.e. 20x*y/100x=y/5
Selected C stays the same --> 6y
Then "total selected" is y/5+6y or 31y/5 --> that's the denominator of the fraction. 
the numerator remains at 6y so now you need to do 6y divided by 31y/5 or 6y*5/31y which equals 30/31. 
Answer E

KumarRishav · Answer

When I use x=4 and y =3, answer is not coming. Why is that?

Krunaal · Answer

x = 4, y = 3. In this case we would have:

20x=80 black-and-white films;
6y=18 color films.

y/x%=(3/4)%=3/400 of the black-and-white films, so 3/5 black-and-white films and all 18 color films, thus total 18 + 3/5 = 93/5 films were selected.

Color films thus compose 18/(93/5) = 90/93 = 30/31 of the selected films.

Answer: E.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards