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help me~

by Goodlife » Thu Aug 07, 2008 8:06 am
help me~ :D

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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.

ans : D

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by sudhir3127 » Thu Aug 07, 2008 8:23 am
My take is D as well..

The daily cost per person for 4 people sharing the cost of a room equally is $45

45 $ for each for 4 = 180 $. hence for 3 people its 60 ( 180 -120)

hence for each its 60/3 = 20... 1 is sufficient


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.

( 120 +X )/2 - ( 120 +3x)/4 = 25
solve for X . X = 20 .. 2 is sufficient.

Hence D.

Hope its clear..
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by singalong » Thu Aug 04, 2011 4:16 am
stupid question but why divide by 2 and 4 in the 2nd statement?
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by GMATGuruNY » Thu Aug 04, 2011 4:44 am
Goodlife wrote:help me~ :D

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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.

ans : D
Here's a way to avoid algebra.

Statement 1: The daily cost per person for 4 people sharing the cost of a room equally is $45.
Total cost = 4*45 = 180.
Total cost - cost for first person = 180-120 = 60.
x = 60/3 = 20.
Sufficient.

Statement 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.
If statement 2 is sufficient, it must confirm the same information given in statement 1.
From statement 1:
If x=20, cost per person for 2 people = (120+20)/2 = 70.
Cost per person for 4 people = 45.
Difference = 70-45 = 25. This works.
Thus, x=20.
If x were equal to any other value, the difference between the two costs would not be 25.
Sufficient.

The correct answer is D.
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by gmatboost » Thu Aug 04, 2011 7:04 am
Singalong:
(120 + x)/2 because the cost for 2 people is 120 + x, so the AVERAGE cost for 2 people is Total/Count = (120 + x)/2

(120 + 3x)/4 because similarly the cost for 4 people is 120 + 3x (3 additional people), so the AVERAGE cost for 4 people is Total/Count = (120 + 3x)/4

This question offers a great opportunity to practice NOT solving for x once you have determined that you can do so.

On Statement 1, once you realize that you know
A) the total is 180
B) Person 1 pays 120
C) The remaining money is split 3 ways
You should recognize that you have enough info to find x and move on

On Statement 2, once you set up (120 + x)/2 = 25 + (120 + 3x)/4 you should move on, since this a linear equation with just one variable.

Mitch is right of course that in this case
If x were equal to any other value, the difference between the two costs would not be 25.
In general though, you should be careful about assuming on DS questions that if the answer from Statement 1 works in Statement 2, then Statement 2 is also sufficient. Statement 2 might have two valid answers, and that might just be one of them.
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