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07 Jun 2022, 08:00
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Difficulty:
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79% (02:45) correct
21%
(03:53)
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based on 28
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Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela, or Susan. Matt and Angela together own twice as many houses as Gavin and Susan own. If Gavin owns 100 more houses than Susan owns, and Matt owns 100 more houses than Angela owns, how many houses does Susan own?
A) 46
B) 142
C) 146
D) 192
E) 242
A) 46
B) 142
C) 146
D) 192
E) 242
genericUser
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07 Jun 2022, 08:24
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Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela, or Susan. Matt and Angela together own twice as many houses as Gavin and Susan own. If Gavin owns 100 more houses than Susan owns, and Matt owns 100 more houses than Angela owns, how many houses does Susan own?
let's set up some equation
(1) \(m+g+a+s=576\)
(2) \(m+a=2*(g+s)\)
(3) \(m=a+100\)
(4) \(g=s+100\)
plug (2) in (1)
\(3*(g+s)=576\) -> \(g+s=192\)
from (4) we get
\(2s+100=192\) -> \(s=46\)
feedback appreciated
A) 46
B) 142
C) 146
D) 192
E) 242
let's set up some equation
(1) \(m+g+a+s=576\)
(2) \(m+a=2*(g+s)\)
(3) \(m=a+100\)
(4) \(g=s+100\)
plug (2) in (1)
\(3*(g+s)=576\) -> \(g+s=192\)
from (4) we get
\(2s+100=192\) -> \(s=46\)
feedback appreciated
A) 46
B) 142
C) 146
D) 192
E) 242
07 Jun 2022, 20:29
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Bunuel
Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela, or Susan. Matt and Angela together own twice as many houses as Gavin and Susan own. If Gavin owns 100 more houses than Susan owns, and Matt owns 100 more houses than Angela owns, how many houses does Susan own?
A) 46
B) 142
C) 146
D) 192
E) 242
A) 46
B) 142
C) 146
D) 192
E) 242
The algebra is plenty manageable if you want to go that route. Know what else is plenty manageable? PITA (Plugging In The Answers)!!
I like trying B and D. Nothing in the answer choices causes me to deviate from that preference, so let's check B.
Susan owns 142. Gavin owns 100 more than Susan, so 242. That's 384 already accounted for, so 192 remain for Matt and Angela, but we are told that Matt and Angela together own twice as many as Gavin and Susan. B is wrong. And we need Susan to own fewer than 142, so we can eliminate C, D, and E.
Answer choice A.
ThatDudeKnowsPITA
