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17 Jul 2015, 01:14
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:41) correct
38%
(01:49)
wrong
based on 439
sessions
History
Date
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Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel if the median is 10 gallons?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
ENGRTOMBA2018
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Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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17 Jul 2015, 04:10
Kudos
Bookmarks
Bunuel
Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel if the median is 10 gallons?
A. 1
B. 2
C. 3
D. 4
E. 5
Kudos for a correct solution.
A. 1
B. 2
C. 3
D. 4
E. 5
Kudos for a correct solution.
Let the 4 barrels be A,B,C,D ---> A+B+C+D = 32 and B+C = 20---> A+D = 12 gallons.
Now lets test the values.
Start with C. Can we have 3 for A ---> 3, B,C,D ---> B+C+D = 29 ---> the maximum we can get is 3,29/3,29/3,29/3 but the median in this case is NOT equal to 10. Thus this choice is not correct and so eliminate choices D and E as well.
Now try choice B, if A =2, we can get B+C+D = 30 and the maximum is 10,10,10 each. This goes well with median = 10 and thus is the correct answer. B is the correct answer with the set as {2,10,10,10}
17 Jul 2015, 07:36
Kudos
Bookmarks
Bunuel
Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel if the median is 10 gallons?
A. 1
B. 2
C. 3
D. 4
E. 5
Kudos for a correct solution.
A. 1
B. 2
C. 3
D. 4
E. 5
Kudos for a correct solution.
4 barrels with average capacity of 8 gallons. Hence Total Capacity is 32 G.
Since Median is 10 i.e, average of 2nd and 3rd barrel is 10 => Sum of 2nd and 3rd barrel is 20, with 10 Gallons each (To keep 1st barrel maximum)
Hence 1st and 4th barrel = 32-20= 12
If the 1st Barrel has to be maximum, the fourth barrel should be as low as possible, but it should be minimum of 10.
Hence => 12-10 = 2
Option (B)
