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

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Jun 08, 2014 7:14 pm

Hello,

Can you please help with this:

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%

OA: B

Let the charge for a single room at Hotel R be 100. So charge for a single room at Hotel P is 75
Let the charge for a single room at Hotel G be x. So charge for a single room at Hotel P ix .9x

It must be true that 75 = .9x
Hence, x = 75/0.9 = 750/9 = 250/3 = approx. 83

Hence, x = 83. Since R = 100, the charge for a single room at Hotel R is about 17% greater. Is this correct?

Thanks a lot,
Sri

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Source: Beat The GMAT — Problem Solving | Sun Jun 08, 2014 7:14 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Jun 08, 2014 8:16 pm

Hi Sri,

You've done everything correct except for the last step.

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 you're TESTing, we have...

(100 - 83)/83 = 17/83

17/85 = 1/5 = 20%

So 17/83 is a little bit bigger than 20%

Final Answer: B

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

Contact Rich at [email protected]

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Jun 08, 2014 9:20 pm

[email protected] wrote:Hi Sri,

You've done everything correct except for the last step.

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 you're TESTing, we have...

(100 - 83)/83 = 17/83

17/85 = 1/5 = 20%

So 17/83 is a little bit bigger than 20%

Final Answer: B

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

Hello Rich,

Thank you very much for your prompt and excellent explanation. I totally overlooked the percentage change part. Thanks for all your help.

Best Regards,
Sri

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 09, 2014 1:33 am

gmattesttaker2 wrote:Hello,

Can you please help with this:

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%

OA: B

A very efficient approach is to convert the percentages to RATIOS.

Hotel P is 25 percent less than Hotel R.
Since P is 3/4 of R, we get:
P/R = 3/4.

Hotel P is 10 percent less than Hotel G.
Since P is 9/10 of G, we get:
P/G = 9/10.

The question stem asks for the relationship between R and G.
Ratios can be MULTIPLIED:
R/G = R/P * P/G.
In the equation above, the values in red CANCEL OUT.
Thus:
R/G = R/P * P/G = 4/3 * 9/10 = 6/5 = 120/100.

Since R/G = 120/100, R is 20% greater than G.

The correct answer is B.

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tass@: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Jun 07, 2014 3:12 am; Thanked: 2 times

by tass@ » Mon Jun 09, 2014 11:53 am

Let R= 120
so P=90
and G=100

Now 120-20/100 =.20
so 20% is the ans

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chetan86: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Sun Mar 31, 2013 9:14 am; Thanked: 2 times

by chetan86 » Tue Jun 10, 2014 1:13 am

Ratio of P:R is 3:4 __(1)
Ratio of P:G is 9:10 __(2)

Multiply (1) by 3 to equalize the ratio of 2 statement
Ratio P:R:G becomes 9:12:10

R is 20% more than G.
Hence answer is B. 20%

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toby001: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Jul 11, 2016 9:33 amFollowed by: 2 members; GMAT Score:680

by toby001 » Fri Nov 18, 2016 6:27 pm

Very efficient answer, as always! Thanks!

GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please help with this:

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%

OA: B
A very efficient approach is to convert the percentages to RATIOS.

Hotel P is 25 percent less than Hotel R.
Since P is 3/4 of R, we get:
P/R = 3/4.

Hotel P is 10 percent less than Hotel G.
Since P is 9/10 of G, we get:
P/G = 9/10.

The question stem asks for the relationship between R and G.
Ratios can be MULTIPLIED:
R/G = R/P * P/G.
In the equation above, the values in red CANCEL OUT.
Thus:
R/G = R/P * P/G = 4/3 * 9/10 = 6/5 = 120/100.

Since R/G = 120/100, R is 20% greater than G.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8212; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Nov 29, 2016 2:50 pm

gmattesttaker2 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 = 0.75r

And

p = 0.9g

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

0.75r = 0.9g

r = 1.2g

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

Answer: B

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Founder and CEO
[email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Dec 08, 2016 8:52 pm

toby001 wrote:Very efficient answer, as always!

On test day, though, don't be afraid to solve with an inefficient answer! After all, sometimes waiting for the train to come takes longer than it would simply to walk to your destination. (And on harder problems, sometimes that train never seems to come!)

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