# Question: Hotel Air Conditioning & Cable

## Comment on Hotel Air Conditioning & Cable

### Hi,

Hi,
Please correct me if I am wrong in my reasoning.
The second statement tells us that 70% of the rooms have cable tv but not air conditioning, so the remainder is 30%

The question stem gives us a solid information that 30% of the rooms have air conditioning. Confronting this two informations we have 70% of the rooms with TV and no AC
The stem tells us that 30% of the rooms have AC.
The logic tells us then that thera aro no rooms with AC and TV together so the anser is 0 and the statement is sufficient

### "The second statement tells

"The second statement tells us that 70% of the rooms have cable tv but not air conditioning, so the remainder is 30%"

This part is correct. However, I think you are misinterpreting what "the remainder is 30%" is referring to.

If 70% of the rooms have cable tv but not air conditioning, then the rooms in the remaining 30% can fall under one of THREE possible cases:
1) The room has cable TV and has AC
2) The room has NO cable TV and has AC
3) The room has NO cable TV and does not have AC

So, even when we combine the given information with statement 2, it's possible to have various conflicting cases. Here are two:

case a: there are 10 rooms with cable TV and AC, and there are 20 rooms with NO cable TV and with AC

case b: there are 15 rooms with cable TV and AC, and there are 15 rooms with NO cable TV and with AC

Cheers,
Brent

### how to solve this problem by

how to solve this problem by Venn diagram approach. I agree you have suggested table approach when we have two options.

### The Venn diagram approach is

The Venn diagram approach is very hard to explain without the use of graphics. Plus, as I stated in the Double Matrix Method lesson, Venn diagrams are not useful when solving complex overlapping sets questions.

### Can we solve this with the

Can we solve this with the rules of probability?
Cheers

### Great question!

Great question!
I don't believe this question can be solve using probability rules.

Cheers,
Brent

### I didn't use the double

I didn't use the double matrix but a simple 2 vin diagram,

since AC+CT+AC&CT must equal to 100%, so statement one is 10%.

### As I mentioned in the Double

As I mentioned in the Double Matrix lesson, Venn diagrams and formulas can be used to solve SOME overlapping sets questions, but the Double Matrix technique will work ALL overlapping such questions.