Official Guide Explanation:
Data Sufficiency #33




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Solution and Metadata

Question: 33
Page: 275
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Profit >
Category 2: Arithmetic > Percents > other
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: Note that we're looking for a number, not a percent or relationship.

Statement (1) is insufficient. It gives us a relationship between two numbers (price and profit), but no actual numbers.

Statement (2) is also insufficient. It gives us a number, but that number is the difference between the number we're looking for and some other number (the merchant's cost) that we don't know.

Taken together, the statements are sufficient. If we call cost c and selling price p, the statements give us the following equations:

p - c = 0.2p (the difference between the selling price and the cost was 20\of the selling price)

p = c + 50 (selling price was $50 more than cost)

That's two linear equations with two variables. From there, we don't need to solve, just recognize that we could. Choice (C) is correct.

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