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by gbb » Sat Mar 21, 2009 6:13 pm
help!

A bag contains five stones, tee of which weigh x pounds each and two of which weigh y pounds each. What is the total weight of the stones?

(i) the heaviest combination o three stones has a total weight of 13 pounds
(ii) the lightest combinationof three stones has a total weight of 12 pounds.

answer E
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Source: — Data Sufficiency |
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by DanaJ » Sat Mar 21, 2009 11:07 pm
1. tells us that the heaviest combination of three stones is 13. Now let's think about this for a moment. You have two cases depending on whether x is smaller or greater than y:

a. x < y means that the heaviest combination of three stones will be achieved by taking the two y stones and one x stone, meaning that 13 = 2y + x.

b. x > y means that you need to take the three x stones in order to get the heaviest combination, or 3x = 12.

Since you have no extra info, this is as far as you can go.


2. tells us that the lightest combination of 3 stones is 12. Again, you have two cases:

a. x < y makes the required combination 2x + y = 12 (you pick the lightest stones and one stone of the second type).

b. x > y makes the lightest combination 3y = 12.

Again, you can't pick between cases and 2 is insufficient.


Take both stmts together to realize that for each case a and b you get a system of equations that can easily be used to solve for x and y:
System a:
2y + x = 13
3x = 12

System b:
2x + y = 13
3y = 12.


But yet again, since you don't have any extra info about whether x is smaller than or greater than y, you can't pick between systems and therefore you can't pick between solutions. This is why E is your answer.
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