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

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

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Updated on: 19 Sep 2017, 05:31
2
34
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Difficulty:

35% (medium)

Question Stats:

78% (02:12) correct 22% (02:24) wrong based on 892 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

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

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20 Jan 2012, 13:26
8
7
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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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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30 Nov 2013, 18:54
3
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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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10 Mar 2014, 22:41
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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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21 Sep 2014, 10:27
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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  [#permalink]

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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  [#permalink]

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Updated on: 25 Feb 2016, 15:23
4
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.
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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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25 Nov 2015, 15:09
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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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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

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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  [#permalink]

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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 = (125-110)/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  [#permalink]

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07 May 2017, 10:44
2

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.

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

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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 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.

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

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

G = 10
P = 9
R = 12

12-10 / 10 * 100% = 20%
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Re: The charge for a single room at Hotel P is 25 percent less  [#permalink]

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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%
Re: The charge for a single room at Hotel P is 25 percent less   [#permalink] 26 Aug 2018, 06:44
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