Official Guide Explanation:
Data Sufficiency #58




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Solution and Metadata

Question: 58
Page: 277
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Other >

Explanation: If we call the number of students in M sm and the number of teachers in M tm and follow the same convention for P, we can set up the two ratios and set them equal to each other:

((sm)/(tm)) = ((sp)/(tp))

We're looking for ((sm)/(sp)).

Statement (1) is insufficient. It tells us that sm = sp + 10,000. Absolute differences don't translate into ratios, though. 10,000 could be half the number of students in M, or 5% of the number in M. (Or any other portion, for that matter.)

Statement (2) is also insufficient. By giving us the student - teacher ratio for M, it also gives us the ratio for P, which is the same. However, it doesn't tell us the relative size of the student body in the two districts.

Taken together, the statements are still insufficient. (2) doesn't give us any insight into the number of students in either district. (1) gives us an absolute difference, but no way to turn that into a ratio. Choice (E) is correct.

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