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Official Guide Explanation:
Data Sufficiency #62
This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.
These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.
Solution and Metadata
Explanation: Statement (1) is sufficient. If each of 4 people pay $45 to share a room, the total cost of the room is 45(4) = 180. Since the cost for the first person is 120, the cost for the additional three people is 60, or $20 each.
Statement (2) is also sufficient. Establishing that is trickier than in (1). The daily cost of each of 2 people sharing a room is:
((120 + x)/2)
That is, the $120 for the first person, plus x for the second person, divided by two, to give us the price per person.
The corresponding cost for four people is:
((120 + 3x)/4)
$120 for the first person, x for each of the other three people, divided by the total number of people.
We know that the price for each of the two people is $25 more than the price for each of the four people, so:
((120 + x)/2) = ((120 + 3x)/4) + 25
No need to delve any further into the algebra--that's a one - variable linear equation. We could solve it, but best to accept that we could find the answer and move on. Choice (D) is correct.
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