250 rooms are booked at a particular hotel for the 17th of May.

Question

250 rooms are booked at a particular hotel for the 17th of May. If the cumulative number of nights these rooms have been booked for is 500, how many rooms have been booked for just 1 night?

(1) 50 of the rooms have been booked for 2 nights.
(2) 60 of the rooms have been booked for 3 or more nights.

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Adit_ · Answer

Tricky problem!

Statement 1:
This is straightforward, just knowing this is clearly not enough to answer how many are booked for one night.
NOT SUFFICIENT

Statement:
This one we know how many are booked for 3 OR MORE nights.
If we knew it was ONLY for 3 nights we can directly say 60*3=180 and calculate using two equations.
However we dont know how many are more than 3 and how many are 3. So the cumulative total could be ANYTHING.
NOT SUFFICIENT.

Now combining both:
Its clear that we know both 2 night and 3 or more nights now. It is a simple case of taking the complement of a probabilty type of scenario.
Total we have 250 room 50 2 nights, 60 3 or more nights, so we can find no,of 1 nights.
SUFFICIENT

Answer:  Option C

ExpertsGlobal5 · Answer

Explanation:  
   
Let the number of rooms booked for exactly 0 nights be w.
Let the number of rooms booked for exactly 1 night be x.
Let the number of rooms booked for exactly 2 nights be y.
Let the number of rooms booked for 3 or more nights be z.
Since 250 rooms are booked: w + x + y + z = 250. (Equation I)
The cumulative number of nights these rooms have been booked for is 500.
  We need to find whether the value of x can be determined.  
 
 Statement (1) 
 
y = 50 (Equation II)
 
From Equation I and Equation II, we have 2 equations with 4 unknown variables. 
 
It is NOT possible to determine with certainty the value of x.   Hence, Statement (1) is insufficient.  
 
 Statement (2) 
 
z = 60 (Equation III)
 
From Equation I and Equation III, we have 2 equations with 4 unknown variables. 
 
It is NOT possible to determine with certainty the value of x.   Hence, Statement (2) is insufficient.  
 
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements. 
 
 Statement (1) and Statement (2) combined  
 
From Equations I, II, and III, we have 3 equations with 4 unknown variables.
 
Also, the   information regarding the cumulative number of nights   these rooms have been booked for, which is 500,   does not help determine the value of x  . If the variable z denoted the number of rooms booked for exactly 3 nights, then we would have the equation 0w + 1x + 2y + 3z = 500, but   since z could be any value greater than 2,   we also cannot use this information to determine the value of x.
 
It is NOT possible to determine with certainty the value of x.   Hence, Statement (1) and Statement (2) combined are insufficient.  
 
  E is the correct answer choice.

nuitnuit2672 · Answer

ExpertsGlobal5 
Umm. no hotel books a room for 0 night.

dhruva09 · Answer

ExpertsGlobal5

How '0' nights is considered a warranted assumption that will be known ? Shouln't this be stated in the problem in some form to make it viable ?

250 rooms are booked at a particular hotel for the 17th of May.

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