GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 Feb 2020, 02:58

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The charge for a single room at Hotel P is 25 percent less

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 398
The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post Updated on: 19 Sep 2017, 05:31
2
47
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (02:09) correct 22% (02:24) wrong based on 687 sessions

HideShow timer Statistics

The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

I solved the the problem as follows:
Let rate in R = 100x
then P = 75x

G = 100y
P = 90y

Thus
75x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%

But I tried first to solve the problem as follows:
p = 100
R = 120
G = 110
and Failed Please help on my second effort.

_________________

Originally posted by Baten80 on 20 Jan 2012, 12:54.
Last edited by abhimahna on 19 Sep 2017, 05:31, edited 1 time in total.
Edited the question
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61537
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 20 Jan 2012, 13:26
9
9
Baten80 wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

I solved the the problem as follows:
Let rate in R = 100x
then P = 75x

G = 100y
P = 90y

Thus
75x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%

But I tried first to solve the problem as follows:
p = 100
R = 120
G = 110
and Failed Please help on my second effort.


As everything is linked with P then: \(0.75R=P=0.9G\) --> \(75R=90G\) --> \(\frac{R}{G}=\frac{90}{75}=1.2\).

Answer: B.

As for your second approach. The numbers are incorrect:
If R=120 then P=90 (not 100);
If G=110 then P=99 (not 100);
If P=100 then R=100/0.75=~133.3 and G=100/0.9=~111.1.
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 18 Sep 2013
Posts: 5
Concentration: Operations, International Business
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Nov 2013, 18:54
4
3
This is a example of Combined Ratios since we need to compare one thing which is common to two other things separately.
Lets consider that charge for Hotel R is $100 then the charge for Hotel P becomes $ 75 (100-75). Similarly considering the charge for Hotel G as $100 the charge for Hotel becomes $ 90 (100-10).
Reducing it to ratios P:R:=75:100 i.e. P:R:=3:4
Similarly P:G:=90:100 i.e. P:G:=9:10
We cannot instantly combine these ratios into a single ratio since the terms for P are different.
So we need to convert these two ratios to combined ration by multiplying first ration with 3 which then becomes 9:12.
Hence the combined ration becomes P:R:G:=9:12:10 which implies that the ratio for R:G is 12:10
So if the charge at Hotel G is $100 then charge at Hotel R becomes $120 or in other words 20% higher.
General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 10 Mar 2014, 22:41
4
2
Answer = B 20%

Please refer below:
Attachments

per.png
per.png [ 6.16 KiB | Viewed 42881 times ]

Intern
Intern
avatar
Joined: 08 Sep 2014
Posts: 2
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 21 Sep 2014, 10:27
1
P = (3/4) R = (9/10) G => R=(6/5) G => R= G+(1/5) G => 20%
Intern
Intern
avatar
Joined: 21 Feb 2015
Posts: 24
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 02 Apr 2015, 18:28
This is how I solved it. Please correct me if I am wrong.
Let R = 100

P= 100*.75= 75 (P is 25% less than R)
G = 75(P) * 1.10 = 82.5 ( G is 10% more than P)

R/G = 100/82.5 = 1.21% Therefore R is 20% greater than G

Alternatively

I can do G/R = 82.5/100 = 82.5% - 1 = 17.5% R is 17.5% greater than G. Looking at choices, I would pick 20%
Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 92
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post Updated on: 25 Feb 2016, 15:23
5
I saw this question at the very end of a GMAC practice test and I had like 30 seconds to do it so this was the fastest way I could come up with:

P=(3/4)R
p=(9/10)G

(9/10)G=(3/4)R
12/10G=R
12/10=20% greater Answer B

Originally posted by DJ1986 on 21 Nov 2015, 17:15.
Last edited by DJ1986 on 25 Feb 2016, 15:23, edited 1 time in total.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16169
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 25 Nov 2015, 15:09
3
2
Hi All,

This question can be solved by TESTing VALUES.

Let's TEST...
The single room charge at Hotel R = $100
The single room charge at Hotel P = $75
The single room charge at Hotel G = about $83

This question uses the phrase "what percent greater…" which means that we have to use the Percentage Change Formula:

Percentage Change = (New - Old)/Old.

In this scenario, the price at Hotel R is the "New" number and the price at Hotel G is the "Old" number.

Using the numbers we're TESTing, we have…

(100 - 83)/83 = 17/83

Since we estimated that "83", the correct answer will be approximately...

17/85 = 1/5 = 20%

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4848
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Nov 2016, 10:30
1
Baten80 wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%


Let \(p\) = \(\frac{3r}{4}\) = \(\frac{9g}{10}\) = \(90\)

So, \(p = 90\) ; \(r = 120\) & \(g = 100\)

Quote:
The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G


\(\frac{120 - 100}{100}*100 = 20\) %

Hence, answer will be (B) 20 %
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Manager
avatar
P
Joined: 13 Oct 2016
Posts: 240
Concentration: Operations, Leadership
GMAT 1: 600 Q44 V28
GMAT ToolKit User
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 06 May 2017, 09:20
Hi Bunuel ,

Thanks for the Clear and crisp explanation. :)

Warm Regards,
Kritesh Singh
Manager
Manager
avatar
S
Joined: 05 Nov 2016
Posts: 82
GMAT ToolKit User
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 06 May 2017, 19:44
1
I've considered P=100(as everything is based on P)
Thus R = 125 and G = 110
% change = (125-110)/125=12
Not sure where am I going wrong. Kindly explain.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16169
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 07 May 2017, 10:44
2
1
Hi umadurga,

You have to be very careful here - especially when dealing with percent change.

To start, the number 100 is NOT "25% less" than 125... it's only 20% less. Since 125 is the 'base' number, you would have to subtract (25% of 125) from 125... and that would not be a 'nice' number (it would be 125 - 31.25 = 93.75).

If you read my post (a few posts up the page from your post), you'll see how you can make R=100 and proceed from there with relatively nice values.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 07 Dec 2017, 16:54
1
Baten80 wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%


We can let the charge for a room at hotel P = p, the charge for a room at hotel G = g, and the charge for a room at hotel R = r.

We are given that the charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. Thus:

p = 0.75r

p = 3r/4

AND

p = 0.9g

p = 9g/10

We need to determine what percent greater the charge is for hotel R than for hotel G. Thus, we need to evaluate (r - g)/g x 100. However, we first need to get variables r and g in terms of p.

r = 4p/3

AND

g = 10p/9

Substitute 4p/3 for r and 10p/9 for g and we have:

(r - g)/g x 100

[(4p/3 - 10p/9)/(10p/9)] x 100

[(12p/9 - 10p/9)/(10p/9)] x 100

[(2p/9)/(10p/9)] x 100

2/10 x 100 = 20 percent

Alternate solution:

We can let the charge for a room at hotel P = p, the charge for a room at hotel G = g, and the charge for a room at hotel R = r.

We are given that the charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. Thus:

p = .75r

And

p = .9g

Since both right-hand expressions are equal to p, we set them equal to each other, and then we solve for r.

.75r = .9g

r = 1.2g

Thus, Hotel R’s rate is 20% greater than Hotel G’s rate.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
181 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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 04 May 2018
Posts: 4
Location: United States
GMAT 1: 750 Q49 V42
GPA: 3.8
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 03 Jun 2018, 11:57
Quick and easy way:

G = 10
P = 9
R = 12

12-10 / 10 * 100% = 20%
Intern
Intern
User avatar
B
Joined: 27 Oct 2017
Posts: 13
Location: Brazil
Concentration: Technology, Strategy
GMAT 1: 600 Q46 V28
GMAT 2: 650 Q46 V34
GPA: 3.32
WE: Consulting (Non-Profit and Government)
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 26 Aug 2018, 06:44
I took picking numbers approach.
I thougth of a number that was multiple of both 3 and 9 for the price of hotel P. I picked 27 (3*9).
Why 3 and 9?
3: if P = 75% of R, if I divide P by three, I'll find the value of 25% of R price, hence I can calculate R.
9: if P = 90% of G, if I divide P by nine, I'll find the value of 10% of G price, hence I can calculate G.

I picked 27 as the price for P. Thus:
R = 36 (27/3*4)
G = 30 (27/9*10)

Then, I calculate how much 6 represents (in %) of 30. x*30/100=6.
x=20%
Answer B.
Intern
Intern
avatar
B
Joined: 08 Sep 2015
Posts: 1
Location: India
Concentration: General Management, Strategy
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 29 Jun 2019, 19:50
P = .75 R ........... (1)
P = .9 G .................(2)

we can equate equation (1) and (2)

.75 R = .9 G

Since the question is asked by what % R is more than G, we can rewrite it as

[R][/G] = [.9][/.75]

or, [R][/G] = 1.2

=> R is 20% more than G [e.g if R =130 and G=100, we can say that R is 30% more than G]

Time taken ~25 sec
Intern
Intern
avatar
B
Joined: 03 May 2019
Posts: 14
GMAT ToolKit User
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Jun 2019, 04:07
1
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

Please tell me where am I wrong?

We have 3 hotels - P, R and G. Let the R hotel price is 100$, so hotel P is 25% less => which is 75$. Hotel G is 10% more expensive than hotel P => 75+10%=82,5$.
So what we have:
Hotel R = 100$
Hotel G = 82,5$

(100$-82,5$)/82,5$=21%

I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61537
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Jun 2019, 04:24
Karastoyanov wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

Please tell me where am I wrong?

We have 3 hotels - P, R and G. Let the R hotel price is 100$, so hotel P is 25% less => which is 75$. Hotel G is 10% more expensive than hotel P => 75+10%=82,5$.
So what we have:
Hotel R = 100$
Hotel G = 82,5$

(100$-82,5$)/82,5$=21%

I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS


If R = 100, then:
P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R)
G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.)
_________________
Intern
Intern
avatar
B
Joined: 03 May 2019
Posts: 14
GMAT ToolKit User
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Jun 2019, 05:05
Bunuel wrote:
Karastoyanov wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

Please tell me where am I wrong?

We have 3 hotels - P, R and G. Let the R hotel price is 100$, so hotel P is 25% less => which is 75$. Hotel G is 10% more expensive than hotel P => 75+10%=82,5$.
So what we have:
Hotel R = 100$
Hotel G = 82,5$

(100$-82,5$)/82,5$=21%

I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS


If R = 100, then:
P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R)
G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.)



Thank you for the quick answer, but where these 250 are from? Thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61537
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

Show Tags

New post 30 Jun 2019, 05:40
Karastoyanov wrote:
Bunuel wrote:
Karastoyanov wrote:
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

Please tell me where am I wrong?

We have 3 hotels - P, R and G. Let the R hotel price is 100$, so hotel P is 25% less => which is 75$. Hotel G is 10% more expensive than hotel P => 75+10%=82,5$.
So what we have:
Hotel R = 100$
Hotel G = 82,5$

(100$-82,5$)/82,5$=21%

I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS


If R = 100, then:
P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R)
G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.)



Thank you for the quick answer, but where these 250 are from? Thanks



The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G:

75 = 9/10*G;
750/9 = G;
250/3 = G.
_________________
GMAT Club Bot
Re: The charge for a single room at Hotel P is 25 percent less   [#permalink] 30 Jun 2019, 05:40

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

The charge for a single room at Hotel P is 25 percent less

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne