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In a group of 100 homeowners [#permalink]
25 Sep 2017, 13:53

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Question Stats:

47% (01:59) correct
52% (00:54) wrong based on 34 sessions

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

Re: In a group of 100 homeowners [#permalink]
16 May 2018, 09:24

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Expert's post

pranab01 wrote:

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

Re: In a group of 100 homeowners [#permalink]
19 Oct 2019, 13:09

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

Re: In a group of 100 homeowners [#permalink]
20 Oct 2019, 05:52

1

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Expert's post

pranab01 wrote:

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

a) 100 – x – y – z

b) 100 – x – y + z

c) x – y – z + 100

d) x + y + z + 100

e) x + y + z – 100

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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