Thanks calgmatter, I finally understood how to solve these types of questions after much searching.

Excellent! Thank you everyone.

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Jamie Nelson
ManhattanGMAT Instructor

Guys, I feel there is an easy way to solve..
Just visualize the van diagram
the equation is

x+2y+3z = 210..... equation (i) (ie 55+75+80) where x indicates households with one one device, y = households with exactly 2 devices, and z = households with exactly 3 devices.

We need to find the maximum and minimum value of z and difference of them is the answer.

we also know x+y+z = 100... equation (ii) (total no of households)

to maximize the value of z, lets take z as 55 since it cant be more than 55.
when z = 55, x = 45. And these two values satisfy both the equations.

Now, to minimize the value of z, we have to maximize y. Lets take y as 90, we will get z = 10. by trial and error y cannot be more than 90 otherwise equation(ii) will not satisfy..

So the answer is 55-10 ie 45


Some people may find this method difficult. But its really easy and I always solve such questions with this method.

I have faced similar question in GPREP though figures were not same. just to confirm that GMAT tests such questions

Wow. That's great and I'm glad it works for you. I have employed a similar strategy for these types of problems.

_________________
Jamie Nelson
ManhattanGMAT Instructor