Official Guide Explanation:
Data Sufficiency #62




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Solution and Metadata

Question: 62
Page: 278
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Algebra > Linear Equations-Two Unk >

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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