Pumps A, B and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously,can fill the tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?
A)1/3
B)1/2
C)2/3
D)5/6
E)1
Answer is E
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amirhakimi
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theCodeToGMAT
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1/A + 1/B = 5/6 - (1)
1/A + 1/C = 2/3 - (2)
1/B + 1/C = 1/2 - (3)
To find: 1/A + 1/B + 1/C
Add (1), (2) & (3)
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/12 = 1
1/A + 1/C = 2/3 - (2)
1/B + 1/C = 1/2 - (3)
To find: 1/A + 1/B + 1/C
Add (1), (2) & (3)
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/12 = 1
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GMATGuruNY
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Let the pool = 18 units.Pumps A, B and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?
A)1/3
B)1/2
C)2/3
D)5/6
E)1
Rate for A+B = w/t = 18/(6/5) = 15 units per hour.
Rate for A+C = w/t = 18/(3/2) = 12 units per hour.
Rate for B+C = w/t = 18/2 = 9 units per hour.
Combining the rates:
(A+B) + (A+C) + (B+C) = 15+12+9 = 36.
2A + 2B + 2C = 36.
A+B+C = 18 units per hour.
Time for A+B+C to fill the pool = w/r = 18/18 = 1 hour.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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gmatclubmember
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In one hour A&B will fill up 5/6th of the tank.
In one hour B&C will fill up 2/3rd of the tank.
In one hour C&A will fill up 1/2nd of the tank.
Combined:
In one hour the pumps (A & B, B & C, and C & A) will fill the (5/6+2/3+1/2)th part of the tank.
=>In one hour 2 * (A, B &C) pumps will fill (5+4+3)/6th (=2)of the tanks
=> In one hour A, B &C will fill the tank to its capacity (1th of the tank).
In one hour B&C will fill up 2/3rd of the tank.
In one hour C&A will fill up 1/2nd of the tank.
Combined:
In one hour the pumps (A & B, B & C, and C & A) will fill the (5/6+2/3+1/2)th part of the tank.
=>In one hour 2 * (A, B &C) pumps will fill (5+4+3)/6th (=2)of the tanks
=> In one hour A, B &C will fill the tank to its capacity (1th of the tank).
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amirhakimi
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Just a little typo I think happened here:
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/6 = 2
(1/A + 1/B + 1/C)=1
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/6 = 2
(1/A + 1/B + 1/C)=1
theCodeToGMAT wrote:1/A + 1/B = 5/6 - (1)
1/A + 1/C = 2/3 - (2)
1/B + 1/C = 1/2 - (3)
To find: 1/A + 1/B + 1/C
Add (1), (2) & (3)
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/12 = 1
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theCodeToGMAT
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Not exactly a typo, you can say a shortcutamirhakimi wrote:Just a little typo I think happened here:
2 ( 1/A + 1/B + 1/C) = (5+4+3)/6 = 12/6 = 2
(1/A + 1/B + 1/C)=1
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