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17 Oct 2008, 10:31
2
15
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:54) correct 27% (01:40) wrong based on 546 sessions

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For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person? (1) The daily cost per person for 4 people sharing the cost of a room equally is$45.
(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people. ##### Most Helpful Community Reply Intern Joined: 05 Dec 2008 Posts: 18 Re: hotel [#permalink] ### Show Tags 12 Dec 2008, 21:30 4 3 Jcpenny wrote: For a convention, a hotel charges a daily room rate of$120 for 1 person and x dollars for each additional person. What is the charge for each additional person?
(1) The daily cost per person for 4 people sharing the cost of a room equally is $45. (2) The daily cost per person for 2 people sharing the cost of a room equally is$25 more than the corresponding cost for 4 people.

Slightly longer explanation:

Statement 1: If the average is $45, then the total cost per day is 4(45) = 180 With 4 people the cost is$120 + x + x + x
So, we get the equation 120 + 3x = 180 (clearly, we COULD solve this equation for x) --> sufficient

Statement 2:
The average cost for 2 people is (120+x)/2
The average cost for 4 people is (120+3x)/4
We know that the first average cost is $25 more than the second average, so we can create the equation (120+x)/2 = (120+3x)/4 + 25 (clearly, we COULD solve this equation for x) --> sufficient Answer: D ##### General Discussion VP Joined: 17 Jun 2008 Posts: 1177 Re: hotel [#permalink] ### Show Tags 17 Oct 2008, 12:41 1 D. Stmt1: obviously sufficient. Stmt2: (120+x)/2 = (120 + 3x)/4 + 25 and we can solve for x. Hence, sufficient. Manager Joined: 03 Sep 2010 Posts: 61 Location: Israel GMAT 1: 660 Q47 V34 GMAT 2: 670 Q48 V34 GPA: 3.2 WE: Operations (Non-Profit and Government) Re: hotel charges a daily room rate [#permalink] ### Show Tags 18 Jan 2011, 10:45 IMO D. A. If for each person the daly rate is 45$ than 45*4=280. 280-120=160 This is the additional payment that the 3 additional people in the room would have to pay. 160/3 is the rate that each of this 3 people would have to pay. Sufficient.
B. The room rate for 2 people = (120+X). The room rate for 4 people= (120+3*Y). In addition we know that X = 25+Y. So we have 2 integers and two equations. Sufficient.
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Re: hotel charges a daily room rate  [#permalink]

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18 Jan 2011, 22:23
It is D.

From (1) :

45 * 4 = 3x + 120 => x = (180 - 120)/3 = 20

From (2) :

120 + x = 120 + 3x
-------- --------- + 25
2 4

240 + 2x = 120 + 3x + 100

=> x = 240 - 220 = 20
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Re: hotel charges a daily room rate  [#permalink]

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19 Jan 2011, 00:39
Not clear with the second statement. Can anybody clear this please.
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Re: hotel charges a daily room rate  [#permalink]

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08 Feb 2011, 10:23
mcmoorthy wrote:
Not clear with the second statement. Can anybody clear this please.

(i) daily cost per person in the case of two persons: (120+x)/2;
(ii) daily cost per person in the case of four persons: (120+3x)/4.

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27 Jul 2013, 10:13
What's the equation for the second statement?
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17 Sep 2019, 06:13
mikegao wrote:
For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person? (1) The daily cost per person for 4 people sharing the cost of a room equally is$45.
(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people. For a convention, a hotel charges a daily room rate of$120 for 1 person and x dollars for each additional person.

What is the charge for each additional person?

(1) The daily cost per person for 4 people sharing the cost of a room equally is $45. Total cost for 4 person = 120 + 3x = 45*4 = 180 x = 60/3 =$20
SUFFICIENT

(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people. $$\frac{120 + x}{2} - \frac{120 + 3x}{4} = 25$$ $$60 + \frac{x}{2} - 30 - \frac{3x}{4} = 25$$ $$5 = \frac{x}{4}$$ x =$20
SUFFICIENT

IMO C
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Re: For a convention, a hotel charges a daily room rate of $120 [#permalink] 17 Sep 2019, 06:13 Display posts from previous: Sort by # For a convention, a hotel charges a daily room rate of$120

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