how to use the Double-Set Matrix (the MGMAT grid method)

[focusgmat]

Resource : GMATclub forum question
Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

* 20
* 25
* 30
* 35
* 40


OA : 25
How to use the Double-Set Matrix (the MGMAT grid method) to solve the problem?
I tried solving the problem, but couldn't get to the solution.

---------------B----------------------NotB

A -------------20%a=25%(200-a)--------a

NotA---------------------------------
--------------200-a--------------------200

I learned the grid method from the strategy guides. This method made the overlapping sets concept very simple. Please can anyone explain to me as to how I can apply the grid method to the above question.
I am retaking my GMAT in 2 weeks.

[anshu.mishra]

Using the grid method only, lets assume x = no. of people who read "A", and y= no. of people who read y

Now, 0.2x = 0.25 y => y =4/5 x

Total no. of people = 200
=> 0.75 y + (either 0.2x or 0.25 y) + 0.8x = 200 ( Use your grid diagram to understand this )
=> x = 125
and y = 100

Hence, the difference sought = 0.75y - 0.8x = 25

[anshu.mishra]

By the way, here was my grid :

Code: Select All Code

             B       |     B'    |
---------------------|-----------|-------------
A     0.2x = 0.25 y  |   0.8x   |     x     

---------------------|----------|-------------
A'     0.75y         |    0

---------------------|----------|-------------           
             y



Thanks
Anshu

[RonPurewal]

look at your grid:

---------------B----------------------NotB

A -------------20%a=25%(200-a)--------a

NotA---------------------------------
--------------200-a--------------------200

i've highlighted the important part in red.
that's an equation that you can solve!
as soon as you solve that equation, you'll have a numerical value of 'a', which you can then plug in and find everything else.