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Water is poured from a full 4-liter

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Water is poured from a full 4-liter

by Brent@GMATPrepNow » Wed Mar 29, 2017 6:04 am
Water is poured from a full 4-liter bucket into three identical glasses until all four containers (the one bucket and the three glasses) are each 2/5 full. What is the capacity, in liters, of one glass?

A) 4/5
B) 3/2
C) 2
D) 12/5
E) 5/2

Answer: C

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by regor60 » Wed Mar 29, 2017 9:32 am
Brent@GMATPrepNow wrote:Water is poured from a full 4-liter bucket into three identical glasses until all four containers (the one bucket and the three glasses) are each 2/5 full. What is the capacity, in liters, of one glass?

A) 4/5
B) 3/2
C) 2
D) 12/5
E) 5/2

Answer: C

Source: www.gmatprepnow.com
Difficulty level: 600

Let X = glass capacity in liters. Each glass is filled to 2/5 capacity so there are 6X/5 liters in the glasses

Since bucket was full at 4 liters and is now 2/5 full, there are 8/5 liters remaining in the bucket

By conservation of mass :), 8/5 liters + 6X/5 liters = 4 liters and

6X/5= 12/5 therefore 6X=12 and X=C
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by Brent@GMATPrepNow » Thu Mar 30, 2017 6:09 am
Brent@GMATPrepNow wrote:Water is poured from a full 4-liter bucket into three identical glasses until all four containers (the one bucket and the three glasses) are each 2/5 full. What is the capacity, in liters, of one glass?

A) 4/5
B) 3/2
C) 2
D) 12/5
E) 5/2
Water is poured from the 4-liter bucket until the bucket is 2/5 full.
This means that 3/5 of the water was POURED OUT
In other words: volume of water POURED OUT = 3/5 of 4 liters = (3/5)(4) = 12/5 liters

Those 12/5 liters of water are poured into 3 identical glasses, so ...
... the volume of water poured into ONE GLASS = 1/3 of 12/5 = (1/3)(12/5) = 12/15 = 4/5 liters
In other words, each glass contains 4/5 of water.

Let C = the capacity of one glass
Since each glass is only 2/5 full, we can write: 2/5 of C = 4/5 liters of water
Rewrite as: (2/5)C = 4/5
Solve: C = (4/5)/(2/5) = (4/5)(5/2) = 2

Answer: C

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by DavidG@VeritasPrep » Thu Mar 30, 2017 6:52 am
Brent@GMATPrepNow wrote:Water is poured from a full 4-liter bucket into three identical glasses until all four containers (the one bucket and the three glasses) are each 2/5 full. What is the capacity, in liters, of one glass?

A) 4/5
B) 3/2
C) 2
D) 12/5
E) 5/2

Answer: C

Source: www.gmatprepnow.com
Difficulty level: 600
We could also do a little fun back-solving. Look at the answer choices. One of them is shining like a beacon of light and easy arithmetic. So test '2.' If each glass has a capacity of 2 liters, and each glass is 2/5 full, then each glass will contain (2/5)*2 = 4/5 liters. There are 3 of them, so that's 3 * (4/5) = 12/5 = 2 2/5 liters. There are a total of 4 liters, so the remaining 1 3/5 is left in the bucket. 1 3/5 = 8/5, and (8/5)/4 = 2/5, so we've got our answer, C
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