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SFtraveler: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Aug 30, 2010 11:51 am

by SFtraveler » Sun Jan 23, 2011 2:38 pm

Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?

Please show steps to answer this problem.

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Source: Beat The GMAT — Problem Solving | Sun Jan 23, 2011 2:38 pm

ezhilkumarank: Moderator; Posts: 92; Joined: Sat Feb 21, 2009 1:20 amFollowed by: 1 member; Thanked: 5 times

by ezhilkumarank » Sun Jan 23, 2011 3:00 pm

SFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?

Please show steps to answer this problem.

Initial Ratio

DVD : BR
7x: 2x

Adding 6 more BR movies changes the ratio to 11:4.

Hence setting up the equation - (2x+6)/7x = 4/11

=> 22x + 66 = 28x
=> 6x = 66 => x =11

Hence the original number of BR movies was 22 and the final number is 28.

Moving this post to PS forum.

"The will-to-do achieves the deed, when the mind that wills is strong indeed"

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sun Jan 23, 2011 3:19 pm

ezhilkumarank wrote:
SFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?

Please show steps to answer this problem.
Initial Ratio

DVD : BR
7x: 2x

Adding 6 more BR movies changes the ratio to 11:4.

Hence setting up the equation - (2x+6)/7x = 4/11

=> 22x + 66 = 28x
=> 6x = 66 => x =11

Hence the original number of BR movies was 22 and the final number is 28.

Moving this post to PS forum.

please move to PS sub-forum.
also to cut on time the same approach with couple of reductions -->

D/B=7/2 AND D/(B+6)=11/4
2D=7B AND 4D=11B+66 --> 2*7B=11B+66 --> B=22

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 23, 2011 7:56 pm

SFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?

Please show steps to answer this problem.

Sneaky but efficient approach:

Since the DVDs are represented by a 7 and an 11 in the two ratios, the number of DVDs must be a multiple of both 7 and 11.
Thus, it is likely that DVDs = 7*11 = 77.
Thus, Blu-rays = 2*11 = 22, giving us the required ratio of 77:22 = 7:2.
To confirm that these values are correct, the new number of Blu-rays = 22+6 = 28, and the new ratio = 77:28 = 11:4.

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