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The charge for a single room at Hotel P is 25 percent less  [#permalink]

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Difficulty:   25% (medium)

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

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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

_________________

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
Math Expert V
Joined: 02 Sep 2009
Posts: 61537
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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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

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

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.
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Intern  Joined: 18 Sep 2013
Posts: 5
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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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.
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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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

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

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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  Joined: 05 Jul 2015
Posts: 92
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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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

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 V
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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]

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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 _________________ Board of Directors D Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4848 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags 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  P Joined: 13 Oct 2016 Posts: 240 Concentration: Operations, Leadership GMAT 1: 600 Q44 V28 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags Hi Bunuel , Thanks for the Clear and crisp explanation. Warm Regards, Kritesh Singh Manager  S Joined: 05 Nov 2016 Posts: 82 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags 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 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 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 _________________ Target Test Prep Representative 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 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 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  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 Quick and easy way: G = 10 P = 9 R = 12 12-10 / 10 * 100% = 20% Intern  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 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  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 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  B Joined: 03 May 2019 Posts: 14 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS Math Expert V Joined: 02 Sep 2009 Posts: 61537 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS If R = 100, then: P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R) G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.) _________________ Intern  B Joined: 03 May 2019 Posts: 14 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags Bunuel wrote: Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS If R = 100, then: P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R) G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.) Thank you for the quick answer, but where these 250 are from? Thanks Math Expert V Joined: 02 Sep 2009 Posts: 61537 Re: The charge for a single room at Hotel P is 25 percent less [#permalink] ### Show Tags Karastoyanov wrote: Bunuel wrote: Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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.
_________________ Re: The charge for a single room at Hotel P is 25 percent less   [#permalink] 30 Jun 2019, 05:40

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