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# Country X imposes a fixed tourist tax of T dollars that adds to a dail

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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
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Quote:
Country X imposes a fixed tourist tax of T dollars that adds to a daily hotel fee. Harry spends three nights in three different hotels in country X: the Savoy, the Futurama and the Mitz. If a night in the Mitz hotel (excluding tax) costs twice as much as a night in the Futurama hotel (excluding tax), then a night in the Savoy hotel (excluding tax) costs how many dollars?

(1) Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel.

(2) For the night in the Futurama hotel he pays 160 dollars (including tax.)

Tax is fixed = T
Hotel charge = Charge + T

M=2F

(1) Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel. insufic

t+m+t+s=560

(2) For the night in the Futurama hotel he pays 160 dollars (including tax.) insufic

t+f=160

(1 and 2) sufic

t+f=160
t+m+t+s=560
3t+m+s+f=720, 3t+3f+s=720, 3(t+f)=720-s, 3(160)=720-s, s=240

Ans (C)
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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
1
Kudos
given
the Savoy = S,
the Futurama =F
and
the Mitz = M
and
M = 2F
clearly insufficient
stmt 1
M+T + S+ T = 560
or M+S + 2T =560
insufficient
2 ) F + T = 160
insufficient
combine

M = 2F
or from 2 , F= 160-T
or M = 2(160-T)
or 320 -2T
put this in 1st stmt
M +S + 2T =560
320-2T +S +2T = 560
or S = 240

hence C
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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
1
Kudos
given that M=2F without tax 'T'

(1) Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel......... M+S+2T=560.....INSUFFICIENT

(2) For the night in the Futurama hotel he pays 160 dollars (including tax.)...F+T=160.....INSUFFICIENT

Combining both we can the value of S,......so sufficient

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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
1
Kudos
need to find night stay cost in S hotel ( excluding tax)
given
M= 2F

#1
Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel.
M+T+T+S= 560
M+2T+S=560
2F+2T+S=560
2*(F+T)+S=560--(a)
insufficient
#2
For the night in the Futurama hotel he pays 160 dollars (including tax.)
F+T=160--(b)
insufficient
from 1 &2
2*(160)+S= 560
S= 560-320 ; 240
IMO C sufficient

Country X imposes a fixed tourist tax of T dollars that adds to a daily hotel fee. Harry spends three nights in three different hotels in country X: the Savoy, the Futurama and the Mitz. If a night in the Mitz hotel (excluding tax) costs twice as much as a night in the Futurama hotel (excluding tax), then a night in the Savoy hotel (excluding tax) costs how many dollars?

(1) Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel.

(2) For the night in the Futurama hotel he pays 160 dollars (including tax.)
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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
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Kudos
Harry Spends three nights, one each at Futurama, F, Mitz, M, and Savoy, S.
M=2F, Tourist Tax is T dollars per night. We are to find cost per night at S.

Statement 1: Harry pays a total of 560 dollars (including tax) for the night at the Mitz hotel and the night at the Savoy hotel.
From statement 1, we can form the following equation: M+S+2T=560 -------(1) but M=2F hence (1) is the same as 2F+S+2T=560 ------(2)
We have one equation three variables, we cannot determine S based on statement 1 alone.

Statement 2: For the night in the Futurama hotel he pays 160 dollars (including tax.)
We can form the following equation based on statement 2: F+T=160------(3)
Clearly insufficient because we have no information about S. Besides there are two variables and 1 equation, so statement 2 alone is insufficient.

1+2
2F+S+2T=560 -------(2)
F+T=160 -------(3)
(3)*2==> 2F+2T=320 ----(4)
(2)-(4)==> S=240.
Both statements when taken together are sufficient.

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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
I got it Answer C as well. But now I have a doubt why it can't be "E" because the the relation of M & F s taxes are not given despite we have a relation for non taxed ones. How can we assume that taxes are doubled as well along with untaxed relation given?

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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
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Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail [#permalink]
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