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A bag contains five stones, three of which weigh x pounds

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A bag contains five stones, three of which weigh x pounds

by BTGmoderatorDC » Mon Nov 18, 2019 4:56 pm
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
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Nov 18, 2019 8:43 pm
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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