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# The charge for a single room at Hotel P is 25 percent less than the ch

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Re: The charge for a single room at Hotel P is 25 percent less than the ch [#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 than the ch [#permalink]
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Re: The charge for a single room at Hotel P is 25 percent less than the ch [#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 Manager Joined: 05 Nov 2016 Posts: 65 Own Kudos [?]: 41 [2] Given Kudos: 18 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] 1 Kudos 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. GMAT Club Legend Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21846 Own Kudos [?]: 11664 [3] Given Kudos: 450 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 than the ch [#permalink] 2 Kudos 1 Bookmarks Expert Reply 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 Joined: 04 Mar 2011 Status:Head GMAT Instructor Affiliations: Target Test Prep Posts: 3043 Own Kudos [?]: 6271 [2] Given Kudos: 1646 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] 2 Kudos Expert Reply 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 Intern Joined: 03 May 2019 Posts: 12 Own Kudos [?]: 15 [1] Given Kudos: 27 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] 1 Kudos 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS Math Expert Joined: 02 Sep 2009 Posts: 92901 Own Kudos [?]: 618681 [0] Given Kudos: 81586 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Expert Reply Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS If R = 100, then: P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R) G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.) Intern Joined: 03 May 2019 Posts: 12 Own Kudos [?]: 15 [0] Given Kudos: 27 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Bunuel wrote: Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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$=21% I do understand logic behind the proper solution, but can anybody give the solution using not proportions, but real money? TJNAKS If R = 100, then: P = 75 (The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R) G = 250/3 ≈ 83.3333. (The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.) Thank you for the quick answer, but where these 250 are from? Thanks Math Expert Joined: 02 Sep 2009 Posts: 92901 Own Kudos [?]: 618681 [0] Given Kudos: 81586 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Expert Reply Karastoyanov wrote: Bunuel wrote: Karastoyanov wrote: The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? A. 15% B. 20% C. 40% D. 50% E.150% Please tell me where am I wrong? We have 3 hotels - P, R and G. Let the R hotel price is 100$, 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. Manager Joined: 14 Jan 2021 Posts: 51 Own Kudos [?]: 8 [0] Given Kudos: 66 Location: France Schools: Harvard '24 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Hi EMPOWERgmatRichC why is for example 120-100/100 and not 120-100/120 I mean in the formula (new - original)/original, how can I decide which one is the original? Many thanks GMAT Club Legend Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21846 Own Kudos [?]: 11664 [1] Given Kudos: 450 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 than the ch [#permalink] 1 Kudos Expert Reply Hi gastoneMIT, When a question asks "what percent greater..." or "what percent less...." the "original" number is the one that you are COMPARING TO. For example... "X is what percent greater than Y" --> (New - Original)/(Original) = (X - Y)/Y Using numbers instead of variables... "120 is what percent greater than 100" --> (New - Original)/(Original) = (120 - 100)/100 GMAT assassins aren't born, they're made, Rich Originally posted by EMPOWERgmatRichC on 30 Mar 2021, 15:58. Last edited by EMPOWERgmatRichC on 31 Mar 2021, 10:40, edited 1 time in total. Director Joined: 04 Jun 2020 Posts: 552 Own Kudos [?]: 67 [0] Given Kudos: 626 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] EMPOWERgmatRichC wrote: 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%

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC

Thank you for your helpful explanation. I followed your approach but was frustrated when I did not get an answer that exactly matched one of the answer choices. I believed that I needed my answer to exactly match the answer choice because I did not see a word such as "approximate" in the question stem. How did you know that it was okay to estimate? Thank you for your time.
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Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink]
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woohoo921 wrote:
EMPOWERgmatRichC wrote:
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 EMPOWERgmatRichC Thank you for your helpful explanation. I followed your approach but was frustrated when I did not get an answer that exactly matched one of the answer choices. I believed that I needed my answer to exactly match the answer choice because I did not see a word such as "approximate" in the question stem. How did you know that it was okay to estimate? Thank you for your time. Hi woohoo921, If you look at the 5 answer choices, you can see that they are fairly 'spread out' percentages - which often means that you can potentially use estimation at some point in your calculations. If the answers had been really 'close' to one another (for example, 19%, 20%, 21%, 22%, 23%), then far more specific calculations would obviously be required (as any type of minor rounding error could lead you to an answer that is too high or too low). GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com Manager Joined: 31 Jan 2020 Posts: 233 Own Kudos [?]: 14 [0] Given Kudos: 139 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Bunuel wrote: 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. Bunuel Does "The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R" not mean : Charge for R - Charge for P = 0.25 Charge for P ? Math Expert Joined: 02 Sep 2009 Posts: 92901 Own Kudos [?]: 618681 [0] Given Kudos: 81586 Re: The charge for a single room at Hotel P is 25 percent less than the ch [#permalink] Expert Reply Tanchat wrote: Bunuel wrote: 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. Bunuel Does "The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R" not mean : Charge for R - Charge for P = 0.25 Charge for P ? Say the charge for a single room at R is$100.

Then the charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R, would mean that the charge for a single room at P is \$75 (25% less than at R).

If you want to express it algebraically, then P = R - 0.25R = 0.75R.

Does this make sense?
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The charge for a single room at Hotel P is 25 percent less than the ch [#permalink]
MHIKER 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%

The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R.

If R=100, then P=75, implying that $$\frac{R}{P} = \frac{100}{75} = \frac{4}{3}$$

The charge for a single room at Hotel P is 10 percent less than the charge for a single room at Hotel G.
If G=100, then P=90, implying that $$\frac{P}{G} = \frac{90}{100} = \frac{9}{10}$$

The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?
$$\frac{R}{G} = \frac{R}{P} * \frac{P}{G} = \frac{4}{3} * \frac{9}{10} = \frac{12}{10}$$

In the resulting ratio, the value of R (12) is 20% greater than the value of G (10).

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