A movie buff owns movies on DVD and on Blu-ray...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A movie buff owns movies on DVD and on Blu-ray...

by BTGmoderatorLU » Tue Mar 13, 2018 3:12 pm

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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?

A. 22
B. 28
C. 77
D. 99
E. 105

The OA is D.

I solved this PS question as follow,

7x / (2x + 16) = 11/4, solve for x => x = 11

Total disks before was 9x = 99.

Experts, any suggestion about it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Tue Mar 13, 2018 3:12 pm

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by [email protected] » Tue Mar 13, 2018 6:37 pm

Hi LUANDATO,

We're told that a movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2 and that if she buys 6 more Blu-ray movies, then that ratio would change to 11:4. We're asked for the original total number of movies in her library BEFORE the extra purchase. This question is based on ratio rules and can be approached in a number of different ways.

To start, since you can't have a 'fraction' of a DVD, the original number of DVDs will be a multiple of 7 and the original number of Blu-rays will be an equivalent multiple of 2...

For example:
7 DVDs and 2 Blu-rays; 9 total
14 DVDs and 4 Blu-rays; 18total
21 DVDs and 6 Blu-rays; 27 total

By extension, the TOTAL number of DVDs and Blu-rays will be a multiple of 9. At this point, you can actually stop working - there's only one answer that's a multiple of 9. The GMAT won't often make it this easy on you to answer this type of question, so some additional math work would likely be required.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 02, 2019 4:25 pm

BTGmoderatorLU 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 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?

A. 22
B. 28
C. 77
D. 99
E. 105

We can let the original number of DVD and Blu-ray she owns be 7x and 2x, respectively. Thus we can create the equation:

7x/(2x + 6) = 11/4

4(7x) = 11(2x + 6)

28x = 22x + 66

6x = 66

x = 11

She originally had 7x + 2x = 9x movies; therefore, she owned 9(11) = 99movies.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
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