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# For a convention, a hotel charges a daily room rate of $120 SORT BY: Tags: Show Tags Hide Tags Intern Joined: 17 Oct 2008 Posts: 7 Own Kudos [?]: 76 [76] Given Kudos: 0 Most Helpful Reply Intern Joined: 05 Dec 2008 Posts: 11 Own Kudos [?]: 22 [17] Given Kudos: 0 Q49 V46 General Discussion Director Joined: 17 Jun 2008 Posts: 614 Own Kudos [?]: 444 [1] Given Kudos: 0 Manager Joined: 03 Sep 2010 Posts: 53 Own Kudos [?]: 78 [0] Given Kudos: 2 Location: Israel GMAT 1: 660 Q47 V34 GMAT 2: 670 Q48 V34 GPA: 3.2 WE:Operations (Non-Profit and Government) Re: hotel charges a daily room rate [#permalink] IMO D. A. If for each person the daly rate is 45$ 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]
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]
Not clear with the second statement. Can anybody clear this please.
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Re: hotel charges a daily room rate [#permalink]
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.
Keeping in view the difference of $25, we make an equation: (120+x)/2 - 25 = (120+3x)/4 240+2x-100 = 120+3x 240-100-120=3x-2x X=20 Retired Moderator Joined: 20 Dec 2010 Posts: 1108 Own Kudos [?]: 4752 [2] Given Kudos: 376 Re: hotel charges a daily room rate [#permalink] 2 Bookmarks Total cost for the room renting; 120 + x*n x - charge per additional person n - number of additional people Q: What is x? 1. (120 + x * 4)/4 = 45. x can be found. Sufficient. 2. (120 + 2*x)/2 = (120+4x)/4 + 25 x can be found. Sufficient. Ans; "D" Manager Joined: 12 Dec 2010 Posts: 79 Own Kudos [?]: 82 [0] Given Kudos: 640 Re: hotel charges a daily room rate [#permalink] Thanks Matt1177!. I got it now Director Joined: 29 Nov 2012 Posts: 576 Own Kudos [?]: 6157 [0] Given Kudos: 543 Re: For a convention, a hotel charges a daily room rate of$120 [#permalink]
What's the equation for the second statement?
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Re: For a convention, a hotel charges a daily room rate of $120 [#permalink] D is correct! Here's why: (1) (120+3x)/4 = 45 --> x = 20 SUFFICIENT (2) (120+x)/2 = 25 + [(120+3x)/4x] --> x = 20 SUFFICIENT GMAT Club Legend Joined: 03 Jun 2019 Posts: 5274 Own Kudos [?]: 4181 [0] Given Kudos: 160 Location: India GMAT 1: 690 Q50 V34 WE:Engineering (Transportation) Re: For a convention, a hotel charges a daily room rate of$120 [#permalink]
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] fluke wrote: Total cost for the room renting; 120 + x*n x - charge per additional person n - number of additional people Q: What is x? 1. (120 + x * 4)/4 = 45. x can be found. Sufficient. 2. (120 + 2*x)/2 = (120+4x)/4 + 25 x can be found. Sufficient. Ans; "D" plz notice the highlighted part (1) (120+3x)/4 = 45 --> x = 20 Manager Joined: 14 May 2023 Posts: 55 Own Kudos [?]: 41 [0] Given Kudos: 9 Location: India Re: For a convention, a hotel charges a daily room rate of$120 [#permalink]
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.

$$\frac{(120+3*x)}{4}=45$$

$$x=20$$

(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. $$\frac{(120+x)}{2}=25+\frac{(120+3x)}{4}$$ $$x=20$$ Both lead to same answers, and individually are sufficient to find charge for each additional person. Hence, Opt (D) Re: For a convention, a hotel charges a daily room rate of$120 [#permalink]
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