GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Mar 2019, 07:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# One night a certain hotel rented 3/4 of its rooms. including

Author Message
TAGS:

### Hide Tags

Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 91
Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

28 Sep 2010, 00:01
1
50
00:00

Difficulty:

95% (hard)

Question Stats:

56% (02:21) correct 44% (02:29) wrong based on 1021 sessions

### HideShow timer Statistics

One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80
Math Expert
Joined: 02 Sep 2009
Posts: 53768
Re: OG 10 Q 248 - % rented  [#permalink]

### Show Tags

28 Sep 2010, 00:09
2
4
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

Consider total # of rooms to be 100;
As 3/5 of the rooms are air conditioned then # of rooms that are air conditioned is 3/5*100=60;

3/4 rooms were rented --> 1/4*100=25 were NOT rented;
2/3 of air conditioned rooms were rented --> 1/3*60=20 air conditioned room were NOT rented;

20/25=4/5=80%.

_________________
##### General Discussion
Manager
Joined: 30 Aug 2010
Posts: 86
Location: Bangalore, India
Re: OG 10 Q 248 - % rented  [#permalink]

### Show Tags

28 Sep 2010, 00:13
This can be easily solved using the matrix method
as the % is asked i can choose a good # for total rooms..let me choose 60 as all the 3 fractions given have 3,4&5 in the denominator and 60 is divisible by all thease 3 #s.

Given:
Total Rented=(60)3/4 = 45
Total AC rooms = (60)3/5 = 36
Total AC rooms rented = (36)2/3 = 24

Plug in:

Rented Not-rented |
|
AC 24 12 | 36
|
|
Non AC |
...............................................................
45 15 | 60

qtn is what % is 12 in 15 = 1200/15 = 80%
Senior Manager
Joined: 18 Sep 2009
Posts: 269
Re: OG 10 Q 248 - % rented  [#permalink]

### Show Tags

28 Sep 2010, 20:48
conditined un condition total

rented 24 21 45

not rent 12 3 15

total 36 24 60

total rooms 60
total rented 60*3/4 =45
total conditioned 60*3/5 =36
total conditioned 36*2/3 24
1200/15=80% (rooms that were not rented were air conditioned
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 353
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: OG 10 Q 248 - % rented  [#permalink]

### Show Tags

28 Sep 2010, 20:56
1
1
The problem will be very easy to solve if you take a 2x2 matrix and work with the given data.

Given fractions - 2/3, 3/4, 3/5 -- L.C.M - 60 [consider this to be the total number of rooms.]

 Rooms Rented Available Total AirCon 24 (Given 2/3 of total aircon) 12 36 (Given - 3/5 of total) NonAircon 21 3 24 Total 45 (Given - 3/4 of total) 15 60 (Total considered)

Hence % of non-rented (available) that were aircon -- 12/15 -- 4/5 -- 80% (E).
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Retired Moderator
Joined: 20 Dec 2010
Posts: 1789

### Show Tags

05 Mar 2011, 12:54
1
Rooms Rented: 3/4
Rooms Not Rented: 1/4

Total AC: 3/5
AC Rented: (2/3)*(3/5) = 2/5
AC Not rented: 3/5 - 2/5 = 1/5.

% of AC that is yet to be rented per total of not rented room;

((1/5)/(1/4))*100 = (4/5)*100 = 80% of remaining(non-rented) rooms are AC.

Ans: "E"
_________________
Manager
Joined: 27 Jul 2010
Posts: 94
GMAT 1: 740 Q50 V40

### Show Tags

05 Mar 2011, 12:59
Let's consider T as the total number of rooms.
If 2/3 of the air conditioned rooms were rented, than 1/3 of them were not rented. We know that the total number of air-conditioned rooms is 3/5, thus we can say that 1/5 of the total rooms in the hotel were air-conditioned and not rented (1/3 x 3/5 = 1/5). (a)

We know that 3/4 of the total rooms were rented, thus 1/4 were not rented. (b)

Using (a) and (b), we can calculate the ratio of air-conditioned rooms to the non-rented rooms: (1/5 x T) / (1/4 x T) = 4/5, and thus non air-conditioned rooms make 80% of the total non-rented rooms.
Senior Manager
Joined: 29 Jan 2011
Posts: 278
Re: OG 10 Q 248 - % rented  [#permalink]

### Show Tags

03 Nov 2011, 03:17
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36

% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)

I am not sure where is my mistake... Can someone please correct me ???
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8998
Location: Pune, India
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

11 Aug 2014, 21:14
siddhans wrote:
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

20
33 1/3
35
40
80

Can someone please explain where am i going wrong here?

Let total rooms be 60

Rented rooms = 3/4 * 60 = 45

Rented AC rooms = 2/3 * 45 = 30

Total AC rooms = 3/5* 60 = 36

% Rooms that are AC and not rented = [(36 - 30) /36] * 100 = 16 * (2/3)

I am not sure where is my mistake... Can someone please correct me ???

"including 2/3rd of their air conditioned rooms" implies that 2/3rd of their air conditioned rooms were a part of the rented rooms.

So if total air conditioned rooms = 36 (as found by you above), 2/3rd of these i.e. 24 of these were rented. So 12 AC rooms were rented.

Total number of rooms that were not rented = 60 - 45 = 15

So AC rooms form what percent of rooms not rented? 12/15 * 100 = 80%
_________________

Karishma
Veritas Prep GMAT Instructor

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1817
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

12 Aug 2014, 00:59
1
1
Refer diagram below (Solved using matrix method)
Going as per serial no (Marked in red) in the matrix

1. Let the total no of rooms = 100

2. 75% rented = 75

3. Not rented = 100-75 = 25

4. $$\frac{3}{5}$$ th of 100 are air conditioned $$= \frac{3}{5} * 100 = 60$$

5. $$\frac{2}{3}$$ rd of air conditioned rooms are AC$$= \frac{2}{3} * 60 = 40$$

6. Not Rented AC rooms = 60-40 = 20

Percentage of Not rented AC rooms $$= \frac{20}{25}* 100 = 80%$$

Attachments

matr.png [ 6.24 KiB | Viewed 15091 times ]

_________________

Kindly press "+1 Kudos" to appreciate

CEO
Joined: 12 Sep 2015
Posts: 3513
One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

Updated on: 28 Apr 2018, 06:56
3
Top Contributor
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

Here's a step-by-step approach using the Double Matrix method.

Here, we have a population of motel rooms, and the two characteristics are:
- air conditioning or no air conditioning
- rented or not rented

So, we can set up our matrix like this:

Now since we're asked to find a certain PERCENTAGE, let's choose a nice value for the total number of motel rooms.
Notice that the question includes the fractions 3/4, 2/3 and 3/5. So, let's choose a number that works well with all of these fractions.
Since 60 is the least common denominator of 3/4, 2/3 and 3/5, let's say that there are 60 motel rooms altogether.

Now that we're set up, we can use the given information to determine the number of rooms to place in each of the four boxes.

If 3/5 of its rooms were air-conditioned
So, 3/5 of the 60 rooms are air conditioned. 3/5 of 60 = 36, which means 36 rooms have AC and the remaining 24 rooms do not have AC...

...motel rented 3/4 of its rooms
3/4 of 60 = 45, so 45 rooms are rented and the remaining 15 rooms are not rented.

...a certain motel rented ....2/3 of its air-conditioned rooms
So of the 36 rooms with AC, 2/3 were rented.
2/3 of 36 = 24. So, 24 rooms had AC AND were rented.

Now that we know the number of rooms in 1 box, and we know the sums of the rows and columns, we can fill in the remaining boxes.

Question: what percent of the rooms that were not rented were air-conditioned?
There were 15 unrented rooms and 12 of them were air conditioned.
12/15 = 4/5 = 80%

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 22 Sep 2016, 12:55.
Last edited by GMATPrepNow on 28 Apr 2018, 06:56, edited 4 times in total.
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 372
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

01 Dec 2016, 18:01
Say we have 60 rooms total:
Rented = 45
Not Rented = 15

Further, we are told that 3/5 of its rooms have A/C
A/C = 36 --> 2/3 of this are included in the rented rooms (above) = 24. So we have 24 Rented A/C Rooms & 12 Rented Non-A/C rooms
No A/C = 24

Overall --> There will be RENTED --> 24 A/C & 12 no A/C --> NOT RENTED --> 12 A/C & 3 no A/C

12/15 = 80%

E.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5380
Location: United States (CA)
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

19 Mar 2018, 16:09
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

We can let the number of rooms = 60. (We choose this convenient number 60 because it is the least common multiple (LCM) of the denominators 3, 4, and 5.)

We see that 3/4 x 60 = 45 rooms were rented and 60 - 45 = 15 rooms were not rented.

We also see that 3/5 x 60 = 36 rooms are air conditioned, and 60 - 36 = 24 rooms are not air conditioned.

Thus, 2/3 x 36 = 24 air conditioned rooms were rented, so 36 - 24 = 12 air conditioned rooms were not rented.

Thus, the percent of rooms that were not rented were air conditioned is 12/15 = 4/5 = 80%.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Director
Joined: 13 Mar 2017
Posts: 704
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

23 Apr 2018, 02:27
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

Let the no. of rooms in the hotel be x.
Total rooms rented = 3/4 x
Total no. of air-conditioned rooms = 3/5 x
Total no. of air-conditioned room that is rented = (2/3)(3/5 x) = 2/5 x

Total no. of air-conditioned room that were not rented = 3/5 x - 2/5 x = 1/5 x

Total no. of room that were not rented = 1/4 x

Percentage of rooms that were not rented were air conditioned = (1/5 x)/(1/4 x) * 100 = 4/5 * 100 = 80%

_________________

CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

VP
Joined: 09 Mar 2016
Posts: 1275
One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

26 Apr 2018, 14:26
1
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

let total number of rooms be $$x$$

total number of rented rooms $$\frac{3}{4}$$x

let total number of AC rooms be $$y$$

AC rented rooms $$\frac{2}{3}$$y

if total number of AC rooms is $$\frac{3}{5} *100 = 60$$

then rented AC rooms is $$\frac{2}{3}*60= 40$$

$$60-40 = 20$$

Hence 20 AC rooms were not rented (perhaps air conditioning was noisy )

now since $$\frac{1}{4} *100 = 25$$ rooms were not rented then

To find what percent of the rooms that were not rented were air conditioned

we just divide number of AC not rented rooms by total number of not rented rooms

$$\frac{20}{25}=0.8$$

pushpitkc, niks18 , generis is my approach correct ?
Senior SC Moderator
Joined: 22 May 2016
Posts: 2558
One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

26 Apr 2018, 15:08
dave13 wrote:
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

let total number of rooms be $$x$$

total number of rented rooms $$\frac{3}{4}$$x

let total number of AC rooms be $$y$$

AC rented rooms $$\frac{2}{3}$$y

if total number of AC rooms is $$\frac{3}{5} *100 = 60$$

then rented AC rooms is $$\frac{2}{3}*60= 40$$

$$60-40 = 20$$

Hence 20 AC rooms were not rented (perhaps air conditioning was noisy )

now since $$\frac{1}{4} *100 = 25$$ rooms were not rented then

To find what percent of the rooms that were not rented were air conditioned

we just divide number of AC not rented rooms by total number of not rented rooms

$$\frac{20}{25}=0.8$$

pushpitkc, niks18 , generis is my approach correct ?

dave13 , well done!

Spot on. Excellent logical reasoning. +1

Quote:
(perhaps air conditioning was noisy )

Hilarious aside.

P.S. I owe you answers . . . I have not forgotten . . .

P.P.S. Here is how I checked your math . . .
Categories, binary choices, fractions and percents?
Fast check? Maxtrix!
Attachment:

dave13matrix2.png [ 9.38 KiB | Viewed 6819 times ]

_________________

And above all, watch with glittering eyes the whole world around you
because the greatest secrets are always hidden in the most unlikely places.
Those who don't believe in magic will never find it
.
—Roald Dahl

Retired Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Re: One night a certain hotel rented 3/4 of its rooms. including  [#permalink]

### Show Tags

27 Apr 2018, 10:24
1
dave13 wrote:
vanidhar wrote:
One night a certain hotel rented 3/4 of its rooms. including 2/3 of their air conditioned rooms. if 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

A. 20
B. 33 1/3
C. 35
D. 40
E. 80

let total number of rooms be $$x$$

total number of rented rooms $$\frac{3}{4}$$x

let total number of AC rooms be $$y$$

AC rented rooms $$\frac{2}{3}$$y

if total number of AC rooms is $$\frac{3}{5} *100 = 60$$

then rented AC rooms is $$\frac{2}{3}*60= 40$$

$$60-40 = 20$$

Hence 20 AC rooms were not rented (perhaps air conditioning was noisy )

now since $$\frac{1}{4} *100 = 25$$ rooms were not rented then

To find what percent of the rooms that were not rented were air conditioned

we just divide number of AC not rented rooms by total number of not rented rooms

$$\frac{20}{25}=0.8$$

pushpitkc, niks18 , generis is my approach correct ?

Hi dave13

generis, has already explained you the matrix method. Here's a small tip from my side - Whenever you see fractions, it's convinient to use SMART Numbers. Here Smart numbers are usually the LCM of denominators.

So we have three fractions here 3/4, 2/3, & 3/5, hence the denominators are 4, 3, 5 whose LCM is 60.

So let the total rooms be 60

So rooms rented $$= \frac{3}{4}*60=45$$

Hence rooms not rented $$= 60-45=15$$

Rooms with AC $$=\frac{3}{5}*60=36$$

AC rooms rented $$= \frac{2}{3}*36=24$$

Hence AC rooms not rented $$= 36-24=12$$

Therefore % of rooms that were not rented and were air conditioned $$= \frac{12}{15}*100 = 80$$%
Non-Human User
Joined: 09 Sep 2013
Posts: 10163
Re: One night a certain hotel rented 3/4 of its rooms. including 2/3 of  [#permalink]

### Show Tags

10 Feb 2019, 23:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 10163
Re: Qn 248 One night a certain motel rented ┬╛ of  [#permalink]

### Show Tags

21 Feb 2019, 22:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Qn 248 One night a certain motel rented ┬╛ of   [#permalink] 21 Feb 2019, 22:12
Display posts from previous: Sort by