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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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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

We can create the equation:

Total = alarm + deadbolt - both + neither

100 = x + y - both + z

both = x + y + z - 100

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