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At a certain hotel, every room has air conditioning or cable TV 20 Sep 2016, 13:54
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55% (hard)

Question Stats:

61% (01:38) correct 39% (01:51) wrong based on 232 sessions

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At a certain hotel, every room has air conditioning or cable TV or both. If 30 percent of the rooms have air conditioning, what percent of the rooms have air conditioning and cable TV?

(1) 80 percent of the rooms have cable TV
(2) 70 percent of the rooms have cable TV but not air conditioning


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A
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At a certain hotel, every room has air conditioning or cable TV 21 Sep 2016, 01:15
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GMATPrepNow
At a certain hotel, every room has air conditioning or cable TV or both. If 30 percent of the rooms have air conditioning, what percent of the rooms have air conditioning and cable TV?

(1) 80 percent of the rooms have cable TV
(2) 70 percent of the rooms have cable TV but not air conditioning

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Answer A. Simple question.

Let total Rooms = 100x

Let a : Only TV
Let b : Both TV and AC
Let c : Only AC.

As per Venn Diagram Rule, We have a + b + c =100x and b + c = AC rooms = 30x

=> a = 70x.

We need to find out % of b.

Statement 1 : a + b = TV Rooms = 80x

or we can say b = 10x = 10%

SUFFICIENT.

Statement 2 : a = 70x. No new information. We already know a is 70x. Hence, insufficient.

Answer A.
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At a certain hotel, every room has air conditioning or cable TV 21 Sep 2016, 02:58
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Dear Abhimanhna
As I am conceiving 30% doesn't says only .....

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At a certain hotel, every room has air conditioning or cable TV 21 Sep 2016, 03:04
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Nikki&sunny
Dear Abhimanhna
As I am conceiving 30% doesn't says only .....

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yes, correct. So, I have taken b+c = 30x.

Added the initial line by mistake. The approach and the solution is correct. I have removed that line now. "We are given c = 30x"
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At a certain hotel, every room has air conditioning or cable TV 21 Nov 2019, 05:38
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At a certain hotel, every room has air conditioning or cable TV or both. If 30 percent of the rooms have air conditioning, what percent of the rooms have air conditioning and cable TV?

(1) 80 percent of the rooms have cable TV
(2) 70 percent of the rooms have cable TV but not air conditioning
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……ac…not…
tv….x……0.7.…
not..………0……
……0.3…0.7…1

(1) 80 percent of the rooms have cable TV sufic

……ac…not…
tv….x…0.7..[0.8] x=0.1
not..………0…0.2
……0.3…0.7…1

(2) 70 percent of the rooms have cable TV but not air conditioning insufic

……ac…not…
tv….x……0.7.…
not..………0……
……0.3…0.7…1

Ans (A)
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At a certain hotel, every room has air conditioning or cable TV 22 Nov 2019, 22:12
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At a certain hotel, every room has air conditioning or cable TV or both. If 30 percent of the rooms have air conditioning, what percent of the rooms have air conditioning and cable TV?

(1) 80 percent of the rooms have cable TV
(2) 70 percent of the rooms have cable TV but not air conditioning

1: A is sufficient
Total = A + T - AT
100 = 30 +80 -AT
AT = 10%

Sufficient

2:

Total= A only + T only +AT
100 = A only + 70 +AT
100 = A - AT +70 +AT
100 = A + 70
A = 30...that we already knows

Not able to find AT = ???

Hence information is not sufficient.

Answer is A
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At a certain hotel, every room has air conditioning or cable TV 19 Feb 2024, 11:28
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Hello from the GMAT Club BumpBot!

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