GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 06:55

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42
Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

30 Jan 2016, 12:56
3
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:15) correct 36% (02:19) wrong based on 81 sessions

HideShow timer Statistics

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.)
Manager
Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

30 Jan 2016, 12:58
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
Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

30 Jan 2016, 21:24
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,

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
_________________
Manager
Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42
Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

31 Jan 2016, 10:44
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?
Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

31 Jan 2016, 10:50
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...
_________________
Manager
Joined: 01 Aug 2014
Posts: 54
Schools: Rotman '17 (A)
GMAT 1: 710 Q44 V42
Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

31 Jan 2016, 11:18
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.
Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

01 Feb 2016, 19:57
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..
_________________
Manager
Joined: 12 Mar 2015
Posts: 82
GPA: 3.9
WE: Information Technology (Computer Software)
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

01 Feb 2016, 22:49
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

Non-Human User
Joined: 09 Sep 2013
Posts: 13392
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail  [#permalink]

Show Tags

18 Oct 2018, 19:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Country X imposes a fixed tourist tax of T dollars that adds to a dail   [#permalink] 18 Oct 2018, 19:25
Display posts from previous: Sort by