Question

The 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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Let us consider x to be the weight of a type X dish and y be the weight of a type Y dish. Thus, we have to determine whether x < y. From statement 1, it is given that 3x + 2y < 2x + 4y, or x < 2y, it is possible that x < y is true (for example, if x = 2 and y = 3) and it is possible that x < y is false (for example, if x = 3 and y = 2). Thus, statement 1 is insufficient. From statement 2, it is given that 4x + 3y < 3x + 4y, it follows that x < y. Thus, statement 2 is sufficient.