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# The weight of an iron bucket increases by 33.33% when filled

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The weight of an iron bucket increases by 33.33% when filled [#permalink]

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26 Aug 2009, 03:30
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17% (00:00) correct 83% (01:12) wrong based on 6 sessions

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The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg
[Reveal] Spoiler: OA
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26 Aug 2009, 03:47
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W=weight of bucket
V=volume of bucket
W + 0,5V = 1,33W
so 0,5V = 0,33W
it wants us (W+V)/2 that is (W + 0,66W)/2= 0,83W But we do not know anything else. So anyone can be. But the sentence in paranthesis gives us a clue. Capacity of bucket and weight of bucket are integer. So W and 0,66W is integer. i.e. W and 2/3W is integer. So we can assume that W is a multiple of 3 (say 3n) . And 0,66 W is a multiple of 2 (say 2n). So they make a multiple of 5 together (3n+2n).
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08 Sep 2010, 03:29
Bunuel, can you please look at this question? I agree with the solution by maliyeci but I don't think that multiple of 2 + multiple of 3 equals multiple of 5 (eg., 18+4 = 22). Thank you.
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08 Sep 2010, 06:55
1
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virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

rets try some numbers.
Say IronB = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
Hope it helps
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08 Sep 2010, 07:05
shaselai wrote:
virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

rets try some numbers.
Say IronB = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
Hope it helps

Hey thanks a lot. My algebra is not that strong, your explanation a lot more sense to me!

Thanks,
Dawgie
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08 Sep 2010, 07:18
Expert's post
virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

$$\frac{bucket}{50% \ water}=\frac{3}{1}$$ --> $$\frac{bucket}{100% \ water}=\frac{3}{1+1}=\frac{3}{2}$$ --> as the weight of bucket and its capacity in kg are integers then the weight of bucket full with water will be a multiple of 3+2=5 (5, 10, 15, 20, ...) --> half of this weight will be 2.5, 5, 7.5, 10, ... Only answer matching this possible values is 5 kg.

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09 Sep 2010, 01:55
Guys, thanks for your explanations but I don't get either.

In shaselai's solution I don't understand if we can pick a different number than 6.

In Bunuel's solution I don't get how he got the first expression.

Thank you.
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09 Sep 2010, 01:59
Expert's post
nonameee wrote:
Guys, thanks for your explanations but I don't get either.

In shaselai's solution I don't understand if we can pick a different number than 6.

In Bunuel's solution I don't get how he got the first expression.

Thank you.

Given that weight of 50% of water is 1/3 (33.33%) of the weight of bucket --> so if bucket=3, then 50% water=1.
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09 Sep 2010, 03:50
Bunuel, thanks a lot. I got it.
Re: Percentage again   [#permalink] 09 Sep 2010, 03:50
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