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The charge for a single room at Hotel P is 25 percent less
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Updated on: 19 Sep 2017, 05:31
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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 and Failed Please help on my second effort.
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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.
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Re: The charge for a single room at Hotel P is 25 percent less
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20 Jan 2012, 13:26
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.
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Re: The charge for a single room at Hotel P is 25 percent less
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30 Nov 2013, 18:54
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 (10075). Similarly considering the charge for Hotel G as $100 the charge for Hotel becomes $ 90 (10010). 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
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10 Mar 2014, 22:41
Answer = B 20% Please refer below:
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Re: The charge for a single room at Hotel P is 25 percent less
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21 Sep 2014, 10:27
P = (3/4) R = (9/10) G => R=(6/5) G => R= G+(1/5) G => 20%



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



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Re: The charge for a single room at Hotel P is 25 percent less
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Updated on: 25 Feb 2016, 15:23
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.



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Re: The charge for a single room at Hotel P is 25 percent less
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25 Nov 2015, 15:09
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
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Re: The charge for a single room at Hotel P is 25 percent less
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30 Nov 2016, 10:30
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 %
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Re: The charge for a single room at Hotel P is 25 percent less
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06 May 2017, 09:20
Hi Bunuel , Thanks for the Clear and crisp explanation. Warm Regards, Kritesh Singh



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Re: The charge for a single room at Hotel P is 25 percent less
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06 May 2017, 19:44
I've considered P=100(as everything is based on P) Thus R = 125 and G = 110 % change = (125110)/125=12 Not sure where am I going wrong. Kindly explain.



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Re: The charge for a single room at Hotel P is 25 percent less
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07 May 2017, 10:44
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
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Re: The charge for a single room at Hotel P is 25 percent less
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07 Dec 2017, 16:54
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 righthand 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
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Re: The charge for a single room at Hotel P is 25 percent less
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03 Jun 2018, 11:57
Quick and easy way:
G = 10 P = 9 R = 12
1210 / 10 * 100% = 20%



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



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Re: The charge for a single room at Hotel P is 25 percent less
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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]
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Re: The charge for a single room at Hotel P is 25 percent less
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30 Jun 2019, 04:07
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



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Re: The charge for a single room at Hotel P is 25 percent less
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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$=21%
I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS If R = 100, then: P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R) G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.)
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Re: The charge for a single room at Hotel P is 25 percent less
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30 Jun 2019, 05:05
Bunuel wrote: Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
A. 15% B. 20% C. 40% D. 50% E.150%
Please tell me where am I wrong?
We have 3 hotels  P, R and G. Let the R hotel price is 100$, 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



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