Official Guide Explanation:
Data Sufficiency #25




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Solution and Metadata

Question: 25
Page: 274
Difficulty: 5 (Moderate)
Category 1: Word Problems > Rate Problems > other

Explanation: Call Carmen's current weekly pay p, which is given as follows:

p = 30x, where x is her hourly rate.

If her hourly rate were increased by $1.50, it would be (x + 1.5). Her new number of hours is h in the following equation:

p = h(x + 1.5)

Note that p remains the same -- the question asks us how many fewer hours she'd need to work to maintain the same weekly pay. The value of figuring out the algebraic representation is that we know how many variables we're working with. We have three variables (p, x, and h), and two equations. If we can get one more equation without adding any new variables, we can answer the question.

Statement (1) is sufficient. If p = 225, we have our third equation. To solve, you can plug p = 225 into the first equation to find x, then plug p and x into the second equation to find h.

Statement (2) is also sufficient. If 1.50 is 20% of her current hourly wage, 1.5 = 0.2x. Again, it's a third equation with no new variables. We can plug in the resulting value of x into the first equation and use the results to find h in the second equation. Choice (D) is correct.

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