"GRE数学题解析：液体价格比较"

In this GRE math problem, we are given that a certain brand of dishwashing liquid is sold in two different bottle sizes: small and large. The small bottle contains 2/5 as many ounces of liquid as the large bottle and is sold at a price that is 1/2 the price of the large bottle. We are asked to compare the price per ounce of the liquid in the small bottle to the price per ounce of the liquid in the large bottle. Let's denote the price of the small bottle as S, the price of the large bottle as L, the volume of the small bottle as V1, the volume of the large bottle as V2, and the price per ounce of the liquid in the small bottle as P1 and in the large bottle as P2. Since the small bottle contains 2/5 as many ounces of liquid as the large bottle, we have: V1 = (2/5)V2 And since the small bottle is sold at half the price of the large bottle, we also have: S = (1/2)L To find the price per ounce of the liquid in each bottle, we divide the price by the volume: P1 = S/V1 = (1/2)L / V1 P2 = L/V2 Plugging in the values of V1 = (2/5)V2 and S = (1/2)L into the equations above, we get: P1 = (1/2)L / (2/5)V2 = (5/4)(L/V2) = (5/4)P2 This shows us that the price per ounce of the liquid in the small bottle (P1) is 5/4 times that of the large bottle (P2). Therefore, Quantity A is greater than Quantity B in this problem. Overall, the solution to this problem involves setting up equations based on the information given, solving for the price per ounce in each bottle, and then comparing the two quantities to determine the relationship between them. This problem illustrates the importance of understanding proportions and ratios in solving mathematical problems.