aa008 wrote:
There are three boxes labelled A, B and C having a total weight of 150 kg. Find the weight of the heaviest box?
1) The sum of the weight of boxes A and B equals twice the weight of box C.
2) The weight of box A equals the sum of the weight of the boxes B and C.
Target question: Find the weight of the heaviest box? Given: There are three boxes labelled A, B and C having a total weight of 150 kg. Let A = weight of box A
Let B = weight of box B
Let C = weight of box C
We can write:
A + B + C = 150 Statement 1: The sum of the weight of boxes A and B equals twice the weight of box C. We can write: A + B = 2C
So, we have the following system:
A + B + C = 150A + B = 2C
Subtract the bottom equation from the top equation to get: C = 150 - 2C
Solve to get C = 50
Notice that box C cannot be the heaviest box, since that would mean A and B are each less than 50, which would make it impossible to have a total weight of 150 pounds.
Since there's no way to find the weight of the heaviest box, statement 1 is NOT SUFFICIENT
If you're not convinced, let's TEST some values
There are several scenarios that satisfy statement 1 (and the equation
A + B + C = 150). Here are two:
Case a: A = 10, B = 90 and C = 50. In this case, the answer to the target question is
the heaviest box weighs 90 poundsCase b: A = 30, B = 70 and C = 50. In this case, the answer to the target question is
the heaviest box weighs 70 poundsSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The weight of box A equals the sum of the weight of the boxes B and C.First off, this tells us that box A is the heaviest box.
We can also write: A = B + C
So, we have the following system:
A + B + C = 150A = B + C
Rewrite as follows:
A + B + C = 150A - B - C = 0
Add the two equations to get: 2A = 150
Solve: A = 75
Since we already concluded that box A is the heaviest, the answer to the target question is
the heaviest box weighs 75 poundsSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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