A dairy farmer has 3 different kinds...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A dairy farmer has 3 different kinds...

by BTGmoderatorLU » Sat Oct 21, 2017 6:39 pm

A dairy farmer has 3 different kinds of milk of quantities: 82 litres, 123 litres, and 205 litres respectively. Find the least number of casks of equal size required to store all the milk without mixing.
Note: The size of each cask should be an integer.

A)9
B)10
C)12
D)15
E) 8

The OA is B.

how can I solve this PS question? Can any expert help with it? Please. Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Oct 21, 2017 6:39 pm

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A diary farmer

by GMATGuruNY » Sun Oct 22, 2017 4:36 am

LUANDATO wrote:A dairy farmer has 3 different kinds of milk of quantities: 82 litres, 123 litres, and 205 litres respectively. Find the least number of casks of equal size required to store all the milk without mixing.
Note: The size of each cask should be an integer.

A)9
B)10
C)12
D)15
E) 8

Total volume of milk = 82 + 123 + 205 = (2*41 + 3*41 + 5*41) = 41(2 + 3 + 5) = 41*10.
The products in blue imply that the three distinct volumes -- 82,123, 205 -- can be stored without mixing in 10 41-liter casks, as follows:
82 liters --> 2 41-liter casks
123 liters --> 3 41-liter casks
205 liters --> 5 41-liter casks.
Thus, the smallest possible number of casks = 2+3+5 = 10.

The correct answer is B.

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by Scott@TargetTestPrep » Wed Nov 20, 2019 6:01 pm

BTGmoderatorLU wrote:A dairy farmer has 3 different kinds of milk of quantities: 82 litres, 123 litres, and 205 litres respectively. Find the least number of casks of equal size required to store all the milk without mixing.
Note: The size of each cask should be an integer.

A)9
B)10
C)12
D)15
E) 8

The OA is B.

how can I solve this PS question? Can any expert help with it? Please. Thanks.

Since the greatest common factor of 82, 123 and 205 is 41, we can let the capacity of each cask be 41 litres, and therefore, the least number of casks needed is 82/41 + 123/41 + 205/41 = 2 + 3 + 5 = 10.

Answer: B

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