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Filling and Leaking Tank

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Filling and Leaking Tank

by alex.gellatly » Sat Jun 23, 2012 7:47 pm
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 < 2x^2 - 4xy + 2y^2

(2) The total capacity of tank 2 is less than one-half that of tank 1.
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by sandeep_thaparianz » Sun Jun 24, 2012 4:39 am
Volume of water in tank 1 after 1 min= (x-y)
Volume of tank 2 =2(x-y)

Now time taken to fill Tank 1 = z/(x-y)
Time taken to fill tank 2 = 2(x-y)/y
Ifor the condition that time taken for filling tank 1 is less than time taken to filltank2
Then z/(x-y) < 2(x-y)/y
Solving this we get statement 1

Hence statement 1 is sufficient

Now statement 2 tells us that 2(x-y)<z/2
Not taking us anywhere I guess. So
OA should be A
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by Anurag@Gurome » Sun Jun 24, 2012 6:19 am
alex.gellatly wrote: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 < 2x^2 - 4xy + 2y^2
(2) The total capacity of tank 2 is less than one-half that of tank 1.
Capacity of T1 = z
Water in T1 after 1 minute = (x - y)
Hence, capacity of T2 = 2(x - y)

Time taken to fill T1 = z/(x - y) minute
Time taken to fill T2 = 2(x - y)/y minute

If T1 fills up before T2,
  • ## z/(x - y) < 2(x - y)/y
    --> yz < 2(x - y)²
Hence, we need to find whether the above condition holds or not.

Statement 1: zy < 2x² - 4xy + 2y²
So, yz < 2(x² - 2xy + y²)
--> yz < 2(x - y)²

Sufficient.

Statement 2: 2(x - y) > z/2 --> z > 4(x - y)
Consider the following two cases,
  • x = 4, y = 2, z = 10 ---> Time to feel T1 = 10/(4 - 2) = 5 > Time to feel T2 = 2(4 - 2)/2 = 2
    x = 4, y = 1, z = 15 ---> Time to feel T1 = 15/(4 - 1) = 5 < Time to feel T2 = 2(4 - 1)/1 = 6
Not sufficient

The correct answer is A.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
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