PS "A movie buff owns movies" question

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pagalmes: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Dec 28, 2009 6:11 am; Thanked: 4 times

by pagalmes » Thu Jan 21, 2010 10:15 am

A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:14. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

- 22
- 28
- 77
- 99
- 105

Any idea how to solve that? I can't find the way to solve that question...

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Source: Beat The GMAT — Problem Solving | Thu Jan 21, 2010 10:15 am

pagalmes: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Dec 28, 2009 6:11 am; Thanked: 4 times

by pagalmes » Thu Jan 21, 2010 10:17 am

Sorry, the questions is the following one (the ratio is 11:4 and not 11:14) :

A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

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pagalmes: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Dec 28, 2009 6:11 am; Thanked: 4 times

by pagalmes » Thu Jan 21, 2010 10:52 am

The answer. You just need to set two equations:

- D / B = 7/2
- D / (B+6) = 11/4

You then just need to solve for D and B.

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BSDesis: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Jan 08, 2010 12:45 pm; Thanked: 1 times

by BSDesis » Fri Jan 22, 2010 9:09 am

pagalmes wrote:Sorry, the questions is the following one (the ratio is 11:4 and not 11:14) :

A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

Hi pagalmes,

I solved the equation like this:

1) D/B = 7/2, -->2D/7B = 1 -->2D=7B --> D=7B/2
2) D/ (B+6) = 11/4 --> (7B/2)/(B+6) = 11/4
3) 7B/2 = (11/4)*(B+6) --> 7B/2=(11B+66)/4 --> [4(7B)]/2=11B+66 --> 28B/2 = 11B+ 66 --> 14B=11B+66 --> 3B=66 --> B=22
4) D/22 = 7/2 --> D=(7*22)/2 --> D=154/2 --> D=77
5) D+B= 77+22 =99 movies

You could perform step 4 a little quicker by realizing that 2*11=22; therefore 7*11=x

Hope that helps.

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Concordio: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue Nov 10, 2009 10:39 am; Thanked: 1 times

by Concordio » Fri Jan 22, 2010 11:03 pm

I did this the same way as described by the above posts, but looking at the answer choices it looks like 99 could be the only choice. The ratio of 7:2 indicates that the original number would have to be divisible by 9. 99 is the only answer choice on the list that fits the original ratio.

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pagalmes: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Dec 28, 2009 6:11 am; Thanked: 4 times

by pagalmes » Sat Jan 23, 2010 11:59 pm

Thanks for your answers!

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Fri Feb 19, 2010 6:12 am

pagalmes wrote:A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 6 more Blu-ray movies, that ratio would change to 11:14. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

- 22
- 28
- 77
- 99
- 105

Any idea how to solve that? I can't find the way to solve that question...

if the ratio is 11:4
so 7x/(2x+6) = 11/4 --> 28x = 22x +66 --> x=11
so original no. = 7x+2x=9x=99

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