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

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

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New post 30 Jan 2016, 11:56
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Question Stats:

64% (02:15) correct 36% (02:23) wrong based on 77 sessions

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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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New post 30 Jan 2016, 11:58
I understand how the above question can be converted to two algebraic equations from which the cost of the Savoy can be derived... What I don't understand is how can the cost excluding tax be derived? Thanks
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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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New post 30 Jan 2016, 20:24
1
Anonamy wrote:
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.)


Hi,

To answer your Query, i will solve it for you..

what does the Q stem tell us..

M = 2F....

lets see the statements..
(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+S+T=560..
Clearly insuff...

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

Combined..
we have two equations...

M+T+S+T=560..
M+S+2T=560...(i)

F+T=160
multiply by 2..
2F+2T=320...
We know M=2F..
so M+2T=320..(ii)

substitute this value in (i).
M+S+2T=560...(i)
M+2T+S=560..
or 320+S=560..
S=240..
This is the value without tax..
ans C

Hope it helps
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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

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New post 31 Jan 2016, 09:44
Correct me if I'm wrong but doesn't stmt 1 state that:

2M + 2T + S + T = 560 <---- tax is counted twice for M for 2 nights

Therefore, in subbing out 2(M + T) and then making S = 240, S = 240 still actually contains S + T = 240?
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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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New post 31 Jan 2016, 09:50
Anonamy wrote:
Correct me if I'm wrong but doesn't stmt 1 state that:

2M + 2T + S + T = 560 <---- tax is counted twice for M for 2 nights

Therefore, in subbing out 2(M + T) and then making S = 240, S = 240 still actually contains S + T = 240?


Hi,
Why would tax be counted twice.
Tax is standard,T, for all three per night...
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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

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New post 31 Jan 2016, 10:18
It doesn't matter if T is a fixed percentage or a fixed amount per night regardless of hotel cost (so by 2T I only meant that it is counted for 2 nights for hotel M), but that wouldn't change that answer C gives S + T = 240 (with tax and not excluding tax)... Unless I am wrong.
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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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New post 01 Feb 2016, 18:57
Anonamy wrote:
It doesn't matter if T is a fixed percentage or a fixed amount per night regardless of hotel cost (so by 2T I only meant that it is counted for 2 nights for hotel M), but that wouldn't change that answer C gives S + T = 240 (with tax and not excluding tax)... Unless I am wrong.


hi,
why are you counting T for two nights for M...
Quote:
If a night in the Mitz hotel (excluding tax) costs twice as much as a night in the Futurama hotel (excluding tax)
..
it is clearly talking of "excluding tax"..

I would request you to go through the solution 2-3 posts above, please tell me where you find some problem, I may be able to help you..
What I can make out is that may be you are reading some aspect wrongly. Please feel free to ask query after going through the solution..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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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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New post 01 Feb 2016, 21:49
Anonamy wrote:
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.)



Let the cost per night at Futurama hotel be x
There cost at Mitz hotel =2x

Stmt1: 2x+ Cost at Savoy + Tax =560 (insuff)
Stm2: x + Tax =160 ( Insuff)

Combining

x= 160- Tax
So 2( 160-Tax) + Cost at Savoy + Tax = 560
Cost at Savoy = 240 + Tax

Answer: C.
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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] 18 Oct 2018, 18:25
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