I was trying to solve the problem using matrix method but I got 100-x-z-y which is wrong. Can anyone show me how to solve this problem using the table matrix method? Thank you

Let's use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of homeowners, and the two characteristics are:
- has alarm security system or does NOT have alarm security system
- has deadbolt locks or does NOT have deadbolt locks

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks.
We can set up our matrix as follows:



z homeowners had neither an alarm security system nor deadbolt locks
We get:



Since the two boxes in the BOTTOM ROW must add to 100-y, we know that the missing box must be 100-y-z, since 100-y-z + z = 100-y



Finally, the two boxes in the LEFT-SIDE column must add to x
In other words, ? + (100-y-z) = x
Subtract (100-y-z) from both sides to get: ? = x - (100-y-z)


Take: x - (100-y-z)
Simplify to get: x - 100 + y + z
Rearrange to get: x + y + z - 100

Answer: E

This question type is VERY COMMON on the GRE, so be sure to master the technique.

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