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reserve tank

by okigbo » Wed Nov 11, 2009 1:07 am
Reserve tank 1 is capable of holding z gallons of water. Water is pumped into tank 1, which starts off empty, at a rate of x gallons per minute. Tank 1 simultaneously leaks water at a rate of y gallons per minute (where x > y). The water that leaks out of tank 1 drips into tank 2, which also starts out empty. If the total capacity of tank 2 is twice the number of gallons of water actually existing in tank 1 after one minute, does tank 1 fill up before tank 2?

(1) zy < 2x2 - 4xy + 2y2

(2) The total capacity of tank 2 is less than one-half that of tank 1
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by okigbo » Wed Nov 11, 2009 1:10 am
(1) zy < 2x^2 - 4xy + 2y^2
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by xcusemeplz2009 » Wed Nov 11, 2009 2:32 am
okigbo wrote:(1) zy < 2x^2 - 4xy + 2y^2
IS IT a???
It does not matter how many times you get knocked down , but how many times you get up
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by aks.anupam » Wed Nov 11, 2009 3:10 am
Tank 1 Capacity: z gallons.
Filling Rate of Tank 1: (x-y) gallons/min

Time required for Tank 1 to fill to capacity(in minutes): Capacity/Rate = z/(x-y)

Tank 2 Capacity: 2(x-y) gallons [twice the number of gallons of water in Tank1 after one minute]
Filling Rate of Tank 2: y gallons/minute

Time required for Tank 2 to fill to capacity(in minutes): Capacity/Rate = 2(x-y)/y

So, we need to find out if

z/(x-y) > 2(x-y)/y

or, zy > 2(x-y)(x-y)
or, zy > 2x^2 + 2y^2 - 4xy

From (1), zy < 2x2 - 4xy + 2y2 (Assuming it is a minus sign between 2x2 & 4xy)
So this is sufficient.

From (2), 2(x-y) < z/2
or, 4(x-y) < z
or, z > 4(x-y)
or, zy > 4xy - y^2

Not sufficient.

So, IMO the answer should be A.

What is the OA?
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by okigbo » Wed Nov 11, 2009 10:46 am
Nice work. Didn't even realize this was a standard work problem. OA:A
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