Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectThe weights of all dishes of type X are exactly the same, and the weights of all dishes of type Y are exactly the same. Is the weight of 1 dish of type X less than the weight of 1 dish of type Y ?
(1) The total weight of 3 dishes of type X and 2 dishes of type Y is less than the total weight of 2 dishes of type X and 4 dishes of type Y.
(2) The total weight of 4 dishes of type X and 3 dishes of type Y is less than the total weight of 3 dishes of type X and 4 dishes of type Y.
Solution:
We are given that we have two types of dishes, dish X and dish Y, and each dish of each type has the same weight. We are asked whether the weight of 1 dish of type X is less than the weight of 1 dish of type Y. If we let X and Y denote the weights of dishes X and Y, respectively, then we can restate the question as:
Is X < Y ?
Statement One Alone:The total weight of 3 dishes of type X and 2 dishes of type Y is less than the total weight of 2 dishes of type X and 4 dishes of type Y.
Using the information from statement one we can set up the following inequality:
3X + 2Y < 2X + 4Y
X < 2Y
We see that the weight of 1 dish of type X is less than the combined weight of 2 dishes of type Y. However we can’t tell whether the weight of 1 dish of type X is less than the weight of 1 dish of type Y. This is not enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:The total weight of 4 dishes of type X and 3 dishes of type Y is less than the total weight of 3 dishes of type X and 4 dishes of type Y.
Using the information from statement two we can set up the following inequality:
4X + 3Y < 3X + 4Y
X < Y
We see that this answers the question.
The answer is B.