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In a group of 100 homeowners
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25 Sep 2017, 13:53
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55% (01:55) correct
45% (00:54) wrong based on 40 sessions
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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?
Re: In a group of 100 homeowners
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16 May 2018, 09:24
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Expert Reply
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
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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
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20 Oct 2019, 05:52
1
Expert Reply
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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