Official Guide Explanation:
Data Sufficiency #27




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Solution and Metadata

Question: 27
Page: 275
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Fractions >

Explanation: After 200 gallons were removed, the amount of oil in the tank was (3/7)c, where c is capacity. Another way of looking at that is that, before the 200 gallons were removed, the amount in the tank was (3/7)c + 200. We're looking for c.

Statement (1) is sufficient. We know that the amount in the tank before the 200 gallons were removed is (3/7)c + 200; we're now told that that's the same as half of capacity, or (1/2)c. We can set those two equal to each other:

(3/7)c + 200 = (1/2)c

Dealing with the fractions would take some time, but you don't need to. Recognize that this is a one - variable linear equation, so you can solve for c.

Statement (2) is also sufficient. We can write this algebraically as well. We know that after the 200 gallons were removed, the result was (3/7)c. That's also 1600 gallons less than capacity, or c - 1600. Since those two expressions represent the same amount of oil, we can set them equal to each other:

(3/7)c = c - 1600

Again, no need to solve; just recognize that you could. Choice (D) is correct.

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