BTGmoderatorDC wrote:A bag contains five stones, three of which weigh x pounds each and two of which weigh y pounds each. What is the total weight of the stones?
Statement (1): The heaviest combination of three stones has a total weight of 13 pounds.
Statement (2): The lightest combination of three stones has a total weight of 12 pounds.
OA E
Source: Veritas Prep
Total weight of the five stones = (3x + 2y) pounds
Let's take each statement one by one.
Statement (1): The heaviest combination of three stones has a total weight of 13 pounds.
=> 3x = 13, if x > y or , if x < y. Insufficient.
Statement (2): The lightest combination of three stones has a total weight of 12 pounds.
=> x + 2y = 12, if x > y or 3x = 12, if x < y. Insufficient.
(1) and (2) together
Case 1: If x > y
From (1), we have 3x = 13 and from (2), we have x + 2y = 12. Thus, x = 13/3 and y = 23/3.
Case 2: If x < y
From (1), we have x + 2y = 13 and from (2), we have 3x = 12. Thus, x = 4 and y = 4.5.
No unique answer. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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