greatest And Lowest Problem !! tough one :(

[vishubn]

PFA


couldnt foloow this

Vishu

[Morgoth]

greatest number of household who have all three = x

80 - 75 = 15
75 - 55 = 20
80 - 55 = 25

x = 15+20+25 = 60

Lowest number = y = 15 [compare which is the lowest among the above cases]


x-y = 60 - 15 = 45.

OA?

[vishubn]

Ya thats the OA
If u could please elaborate a bit more on this part

80 - 75 = 15
75 - 55 = 20
80 - 55 = 25

Vishu

[gmat009]

greatest number of household who have all three = x

80 - 75 = 15
75 - 55 = 20
80 - 55 = 25

x = 15+20+25 = 60

Lowest number = y = 15 [compare which is the lowest among the above cases]


x-y = 60 - 15 = 45.

OA?

CAn you plz. explain this.

[Morgoth]

I apologize for the strange method used. Even though I got the correct answer method used is incorrect. Dont know what I was thinking.

Here is why

Since 55 MP3 at least, the maximum number with all three cannot be 60.

Here is the actual method rather correct method

x = maximum = 55

Maximum people with at least 3 - maximum number with no three = minimum = y

maximum without all three
75-55 = 20 no MP3
80-55 = 25 no MP3

55 - 45 = 10

x-y = 55-10 = 45.


Hope its clear.

[adxb]

I understand how you got x, but I am still confused about how you determined y?

[Ian Stewart]

Clearly the maximum number that could have all three devices is 55; that is, the 55 people who own an MP3 player could also each own a DVD player and a cell phone. So x = 55.

To find y, we need to minimize the number of people who own all three devices. If 80 people own a cell phone, and 75 own a DVD player, let's find the smallest possible number that might own both. We'd want to be sure that all 20 people who do *not* own a cell phone *do* own a DVD player. We'd then have:

own cell, do not own DVD: 25
own DVD, do not own cell: 20
own DVD and cell: 55

Now we have 55 who own both a DVD and a cell. We also know that 55 own an MP3 player. Again, to find the smallest number who own an MP3, a cell and DVD, we want to be sure that all 45 people who do *not* own an MP3 *do* own a cell+DVD. So we have:

owns cell+DVD, but no MP3: 45
owns MP3, but no cell+DVD: 45
owns all three: 10

So at least 10 people must own all three devices, and y = 10.

Finally, x - y = 45.