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

Question

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

abhimahna · Answer

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.

Nikki&amp;amp;sunny · Answer

Dear Abhimanhna
As I am conceiving 30% doesn't says only .....

Sent from my XT1033 using  GMAT Club Forum mobile app

abhimahna · Answer

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"

exc4libur · Answer

……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..  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)

JiddiHuMain · Answer

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

Smriti9 · Answer

but 70% of room has cable and not AC. Hence both =0. Why is B not sufficienrt?

Bunuel · Answer

(2) 70 percent of the rooms have cable TV but not air conditioning 
 
The above means that 70% have  only  cable TV, not AC. The other 30% have AC, but we do not know how many of those also have cable TV. So we cannot determine how many rooms have both.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards