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Post subject: GMAT Overlapping Sets Posted: Mon Aug 02, 2010 7:18 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

In a 100unit student dormitory building, 75 dorm rooms have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. Every dorm room has at least one of these three devices. If x and y are respectively the greatest and lowest possible number of dorms that have all three of these devices, x – y is:
A. 65 B. 55 C. 45 D. 35 E. 25
x, the greatest possible number of dorms that have all three devices, is simply the number of dorms that have at least one MP3 player. After all, it is possible that these 55 dorms (that have an MP3 player) also have a DVD player and a cell phone. Thus, x = 55.
Finding the value of y takes a little more thought: If we add up 80 and 75 we get 155. There are only 100 dorms, so at absolute minimum, there is an overlap of 55. 155 – 100 = 55 dorms must have both a DVD player and a cell phone. We also know that 100 – 55 = 45 dorms do not have an MP3 player, and it is possible that all of these dorms is among the 55 dorms that have both a DVD player and a cell phone. This means that, at minimum, 10 dorms (55 – 45) have an MP3 player, DVD player and cell phone.
Therefore y = 10 and x – y = 45, choice (C)  Kindly can you provide much more detail explanation how the minimum value y is 10.


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Gennadiy

Post subject: Re: math (test 5, question 23): sets, venn diagram. Posted: Mon Aug 02, 2010 9:03 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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