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Buckets X and Y contained only water and bucket Y was 1/2

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Director
Joined: 29 Nov 2012
Posts: 675
Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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21 Jan 2013, 01:26
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84% (01:02) correct 16% (01:02) wrong based on 105 sessions

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Buckets X and Y contained only water and bucket Y was 1/2 full. If all of the water in bucket X was then poured into bucket Y, what fraction of the capacity of Y was then filled with water?

(1) Before the water from X was poured, X was 1/3 full
(2) X and Y have the same capacity.

Kindly provide detailed explanations, thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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21 Jan 2013, 01:51
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Buckets X and Y contained only water and bucket Y was 1/2 full. If all of the water in bucket X was then poured into bucket Y, what fraction of the capacity of Y was then filled with water?

(1) Before the water from X was poured, X was 1/3 full. We cannot simply add 1/3 and 1/2 here because we don't know the capacity of bucket X. Not sufficient.

(2) X and Y have the same capacity. We don't know how much water bucket X has. Not sufficient.

(1)+(2) Since from (2) X and Y have the same capacity, then 1/3 of X = 1/3 of Y, thus fraction of Y filed after pouring is 1/3+1/2=5/6. Sufficient.

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Re: Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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23 Jan 2013, 00:38
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fozzzy wrote:
Buckets X and Y contained only water and bucket Y was 1/2 full. If all of the water in bucket X was then poured into bucket Y, what fraction of the capacity of Y was then filled with water?

(1) Before the water from X was poured, X was 1/3 full
(2) X and Y have the same capacity.

Kindly provide detailed explanations, thanks!

Its given that, Buckets X and Y contained only water and bucket Y was 1/2 full. At this point we dont know the "relative" sizes of buckets X & Y (which one is larger/smaller by how much).

(1) Before the water from X was poured, X was 1/3 full
INSUFFICIENT: This doesn't give the relative size of X to Y. We dont know whether X has more/less capacity than Y.
(2) X and Y have the same capacity.
INSUFFICIENT: We dont know how much water was poured from X to Y.

Combining (1) & (2)
SUFFICIENT: Statement(2) confirms the X=Y in capacity. Statement(1) states the information that X's 1/3 water was poured into Y. This information is sufficient to add 1/2+1/3=5/6. i.e. Y was filled with 5/6 capacity once the water was poured from X to Y

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Joined: 16 Jul 2019
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Re: Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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12 Feb 2020, 09:30
Bunuel, can you please explain if the capacities are different, what difference will it make? I don't get how statement 1 is insufficient.

I just added 1/3+1/2, and concluded that it's sufficient.

Thanks!
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Posts: 62289
Re: Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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12 Feb 2020, 23:15
Rocknrolla21 wrote:
Bunuel, can you please explain if the capacities are different, what difference will it make? I don't get how statement 1 is insufficient.

I just added 1/3+1/2, and concluded that it's sufficient.

Thanks!

Say the capacity of X = 10000000000000000000000000000000000 liters and the capacity of Y = 1 liters. Would Y be 1/3+1/2=5/6 filled with water after 1/3rd of X is poured, to Y?

Or say, the capacity of X = 1 liters and the capacity of Y = 1000000000000000000000000000000 liters. Would Y be 1/3+1/2=5/6 filled with water after 1/3rd of X is poured, to Y?
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Re: Buckets X and Y contained only water and bucket Y was 1/2  [#permalink]

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13 Feb 2020, 01:07

Thank you!
Re: Buckets X and Y contained only water and bucket Y was 1/2   [#permalink] 13 Feb 2020, 01:07
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