* In a village of 100 households - PS Problem

[sudhansu9dm]

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

[jnelson0612]

Excellent! Thank you everyone.

[pitchaivijay]

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

[jnelson0612]

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

[gorla.raghunath]

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

I found a very easy way of solving it:

Let d, c, m indicates no of DVD's, Cell Phone and MP3 users respectively.

p, q, r : Set of two as usually drawn in Venn diagram (coudn't find a way of uploading the picture):

x : All three

As usually as we solve the 3-D venn diagram, we will get the following eqns:

p+q+r+x+d+c+m = 100 ---(1)
p+q+r+x+d = 75
q+r+x+c+c = 80
p+r+x+m = 55

Summing the above 3:
2(p+q+r) + 3x + d+c+m = 210 ---(2)

Now solving 1 and 2

we get : p+q+r+2x = 110

Maximizing x : 2x can be at max 100 so X = 50
Minimizing x : p+q+r can be max 100 so Y = 5

X-Y = 45

[tim]

let us know if there are any further questions on this one..