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At a certain hotel, every room has air conditioning or cable TV

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At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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20 Sep 2016, 13:54
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Difficulty:

55% (hard)

Question Stats:

59% (01:40) correct 41% (01:57) wrong based on 76 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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At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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21 Sep 2016, 01:15
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GMATPrepNow wrote:
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

Kudos for all correct solutions

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.

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Re: At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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21 Sep 2016, 02:58
1
Dear Abhimanhna
As I am conceiving 30% doesn't says only .....

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Re: At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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21 Sep 2016, 03:04
Nikki&amp;sunny wrote:
Dear Abhimanhna
As I am conceiving 30% doesn't says only .....

Sent from my XT1033 using GMAT Club Forum mobile app

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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Re: At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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21 Nov 2019, 05:38
GMATPrepNow wrote:
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

……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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Re: At a certain hotel, every room has air conditioning or cable TV  [#permalink]

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22 Nov 2019, 22:12
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.

Re: At a certain hotel, every room has air conditioning or cable TV   [#permalink] 22 Nov 2019, 22:12
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