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.\(150\%\)
Answer: B
Source: GMAT Prep
The charge for a single room at Hotel \(P\) is \(25\) percent less than the charge for a single room at Hotel \(R\) and
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Solution:Vincen wrote: ↑Wed Mar 31, 2021 7:33 amThe 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.\(150\%\)
Answer: B
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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