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# There are three boxes labelled A, B and C having a total weight of 150

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There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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Updated on: 02 Dec 2018, 22:42
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45% (medium)

Question Stats:

63% (01:26) correct 37% (01:34) wrong based on 95 sessions

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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.

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Originally posted by aa008 on 02 Dec 2018, 21:15.
Last edited by Bunuel on 02 Dec 2018, 22:42, edited 1 time in total.
Renamed the topic.
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Re: There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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02 Dec 2018, 22:30
Given A+B+C = 150

From statement 1:

A+B = 2C
3C = 150
C = 50.
Insufficient.

From statement 2:

A = B+C
2A = 150
A = 75.
Now remaining weight = 150-75 = 75 = B+C
Hence A is the heaviest box.

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Re: There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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03 Dec 2018, 10:13
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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 = 150
A + 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 pounds
Case b: A = 30, B = 70 and C = 50. In this case, the answer to the target question is the heaviest box weighs 70 pounds
Since 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 = 150
A = B + C

Rewrite as follows:
A + B + C = 150
A - 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 pounds
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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03 Dec 2018, 14:54
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.

Question: write down A + B + C = 150, heaviest = ?

Statement 1: This is 'GMAT code'. If the sum of A and B equals twice C, then C's weight is the average of A and B. Since there are only three boxes, that means C is 'right in the middle'. The problem is, we don't know whether A is the heavier box, or whether B is the heavier box. We also don't know whether the weights are (for instance) 1, 50, and 99, or 50, 50, and 50. (Interestingly, if they asked us for the weight of the middle box, this would be sufficient!)

Statement 2: Now we know that A is the heaviest, since it definitely has to be heavier than the other two. Also, since A weighs as much as the other two boxes put together, it must account for half of the total weight. A weighs 75 kg - the statement is sufficient.
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There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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06 Dec 2018, 03:02
GMATPrepNow and ccooley

I am confused...

For S(2) what I also got $$A=B+C$$ and $$A=75$$ and $$B+C=75$$, BUT nowhere is it mentioned that each box contains any weight...
Therfore it could also be that $$B=0$$, in that case $$A$$ and $$C$$ would booth equal 75kg, therefore statement 2 is INSUFFICIENT.

Shouldn't the OA be C?

Only with both statements we know that $$A$$ is not equal to $$C$$...

Can you help me out???
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Re: There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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06 Dec 2018, 07:00
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T1101 wrote:
GMATPrepNow and ccooley

I am confused...

For S(2) what I also got $$A=B+C$$ and $$A=75$$ and $$B+C=75$$, BUT nowhere is it mentioned that each box contains any weight...
Therfore it could also be that $$B=0$$, in that case $$A$$ and $$C$$ would booth equal 75kg, therefore statement 2 is INSUFFICIENT.

Shouldn't the OA be C?

Only with both statements we know that $$A$$ is not equal to $$C$$...

Can you help me out???

I guess to 100% ambiguity, the question COULD mention something about how the boxes weigh more than zero points.
That said, one might also argue that it's impossible for a box to have zero weight.
Then again, if the box contained balloons filled with helium, the box would have zero weight.

This isn't an official GMAT question, but my guess is that the official test-makers would be certain to remove any possible ambiguity.

Cheers,
Brent
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Re: There are three boxes labelled A, B and C having a total weight of 150  [#permalink]

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27 Jan 2020, 19:58
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.

Given: a+b+c=150 -----(i)

(1) a+b = 2c
therefore, c = 50 and a+b=100
case1: a = 50, b=50
case 2: a=70, b = 30
Not Sufficient

(2) a = b+c
Therefore, a = 75 and b+c = 75
Hence, a must be heaviest among the three. Sufficient

B is correct
Re: There are three boxes labelled A, B and C having a total weight of 150   [#permalink] 27 Jan 2020, 19:58
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