Official Guide Explanation:
Data Sufficiency #108




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Solution and Metadata

Question: 108
Page: 161
Difficulty: 5 (Moderate)
Category 1: Algebra > Equations >
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: Since all paperbacks are the same price and all hardbacks are the same price, we're looking for the value of p + h. Statement (1) in insufficient: it tells us that 2p + 3h = $12.50, which isn't enough to find the value of p + h. Statement (2) is also insufficient: if 4p + 6h = $25, we still can't find p + h.

Taken together, the statements are still insufficient. To find the values of two variables, you need two distinct linear equations. These are two linear equations, but they are not distinct. 4p + 6h = $25 is just two times the first equation, 2p + 3h = $12.50. To watch out for this common trap, keep an eye out for the ratio of the coefficients: in the first equation it's 2:3; in the second, it's 4:6, or 2:3. If the ratios are the same, it's very likely that the equations are the same. Choice (E) is correct.

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