Official Guide Explanation:
Data Sufficiency #13

Background

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Solution and Metadata

Question: 13
Page: 154
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Word Problems > Other >

Explanation: If k employees shared the cost equally and we say that each of the k employees spent d dollars each, the total cost is kd. We can ignore n entirely, which isn't relevant to the answer, and doesn't recur in either statement.

Statement (1) is insufficient. It tells us that d = 19, but without the value of k, we can't calculate kd.

Statement (2) is also insufficient. It tells us that (k + 1)18 is equal to the total cost of the dinner. In other words: (k + 1)18 = kd, which still has two variables in one equation.

Taken together, the statements are sufficient. Given that d = 19, we can solve the equation given in (2):

18(k + 1) = 19k

18k + 18 = 19k

18 = k

Since we know d as well, we can calculate the total cost of the dinner. Choice (C) is correct.

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