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# In a group of 100 homeowners

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

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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
[Reveal] Spoiler: OA

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Re: In a group of 100 homeowners [#permalink]  26 Sep 2017, 02:10
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Expert's post
$$X + Y - Both + Neither = 100$$

$$X + Y -B + Z = 100$$

$$X + Y + Z -100 = B$$

E is the winner.

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

We can create the equation:

Total = alarm + deadbolt - both + neither

100 = x + y - both + z

both = x + y + z - 100

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# Jeffrey Miller

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

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:

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

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

RELATED VIDEO FROM MY COURSE

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Brent Hanneson – Creator of greenlighttestprep.com

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Re: In a group of 100 homeowners [#permalink]  20 Oct 2019, 07:09
Expert's post
The king of the matrix is back
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Re: In a group of 100 homeowners   [#permalink] 20 Oct 2019, 07:09
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