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555-605 (Medium)|   Word Problems|         
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mikegao
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For a convention, a hotel charges a daily room rate of $120 17 Oct 2008, 10:31
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D
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25% (medium)

Question Stats:

78% (01:52) correct 22% (01:49) wrong based on 2612 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.
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D
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brenthanneson
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For a convention, a hotel charges a daily room rate of $120 12 Dec 2008, 21:30
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Jcpenny
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.
Show more

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
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scthakur
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For a convention, a hotel charges a daily room rate of $120 17 Oct 2008, 12:41
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D.

Stmt1: obviously sufficient.
Stmt2:
(120+x)/2 = (120 + 3x)/4 + 25 and we can solve for x. Hence, sufficient.
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For a convention, a hotel charges a daily room rate of $120 18 Jan 2011, 10:45
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IMO D.
A. If for each person the daly rate is 45$ 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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For a convention, a hotel charges a daily room rate of $120 18 Jan 2011, 22:23
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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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For a convention, a hotel charges a daily room rate of $120 19 Jan 2011, 00:39
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Not clear with the second statement. Can anybody clear this please.
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Matt1177
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For a convention, a hotel charges a daily room rate of $120 08 Feb 2011, 10:23
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mcmoorthy
Not clear with the second statement. Can anybody clear this please.
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(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
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For a convention, a hotel charges a daily room rate of $120 08 Feb 2011, 10:52
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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"
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For a convention, a hotel charges a daily room rate of $120 08 Feb 2011, 23:26
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Thanks Matt1177!. I got it now :)
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For a convention, a hotel charges a daily room rate of $120 27 Jul 2013, 10:13
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What's the equation for the second statement?
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For a convention, a hotel charges a daily room rate of $120 18 Sep 2016, 08:33
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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
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For a convention, a hotel charges a daily room rate of $120 17 Sep 2019, 06:13
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mikegao
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.
Show more

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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For a convention, a hotel charges a daily room rate of $120 22 Nov 2019, 13:53
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fluke
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"
Show more


plz notice the highlighted part
(1) (120+3x)/4 = 45 --> x = 20
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For a convention, a hotel charges a daily room rate of $120 01 Jul 2023, 18:37
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mikegao
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?
Show more
(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)
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For a convention, a hotel charges a daily room rate of $120 29 Mar 2026, 19:17
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