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sana.noor
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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.
OA is A
according to explanations the capacity of tank 1 is z gallons, however question says that the capacity of reserve tank is z gallons. explanation says that capacity of tank 2 is (x-y). i mean this is totally a confusing question, i need help
Manhattan explanation:
If water is rushing into tank 1 at x gallons per minute while leaking out at y gallons per minute, the net rate of fill of tank 1 is x - y. To find the time it takes to fill tank 1, divide the capacity of tank 1 by the rate of fill: z / (x - y).
We know that the rate of fill of tank 2 is y and that the total capacity of tank 2 is twice the number of gallons remaining in tank 1 after one minute. After one minute, there are x - y gallons in tank 1, since the net fill rate is x - y gallons per minute. Thus, the total capacity of tank 2 must be 2(x - y).
The time it takes to fill tank two then is
2(x - y)/y.
The question asks us if tank 1 fills up before tank 2.
We can restate the question: Is
z/x - y < 2(x - y)/y ?
(1) SUFFICIENT: We can manipulate zy < 2x2 - 4xy + 2y2:
zy < 2x2 - 4xy + 2y2
zy < 2(x2 - 2xy + y2)
zy < 2(x - y)(x - y) (dividing by x - y is okay since x - y > 0)
zyx - y<2(x - y)
(dividing by y is okay since y > 0)
z/x - y<2(x - y)/y
This manipulation shows us that the time it takes to fill tank 1 is definitely shorter than the time it takes to fill tank 2.
(2) INSUFFICIENT: We can express this statement algebraically as: 1/2(z) > 2(x - y). We cannot use this expression to provide us meaningful information about the question.
The correct answer is A.
(1) zy < 2x2 - 4xy + 2y2
(2) The total capacity of tank 2 is less than one-half that of tank 1.
OA is A
according to explanations the capacity of tank 1 is z gallons, however question says that the capacity of reserve tank is z gallons. explanation says that capacity of tank 2 is (x-y). i mean this is totally a confusing question, i need help
Manhattan explanation:
If water is rushing into tank 1 at x gallons per minute while leaking out at y gallons per minute, the net rate of fill of tank 1 is x - y. To find the time it takes to fill tank 1, divide the capacity of tank 1 by the rate of fill: z / (x - y).
We know that the rate of fill of tank 2 is y and that the total capacity of tank 2 is twice the number of gallons remaining in tank 1 after one minute. After one minute, there are x - y gallons in tank 1, since the net fill rate is x - y gallons per minute. Thus, the total capacity of tank 2 must be 2(x - y).
The time it takes to fill tank two then is
2(x - y)/y.
The question asks us if tank 1 fills up before tank 2.
We can restate the question: Is
z/x - y < 2(x - y)/y ?
(1) SUFFICIENT: We can manipulate zy < 2x2 - 4xy + 2y2:
zy < 2x2 - 4xy + 2y2
zy < 2(x2 - 2xy + y2)
zy < 2(x - y)(x - y) (dividing by x - y is okay since x - y > 0)
zyx - y<2(x - y)
(dividing by y is okay since y > 0)
z/x - y<2(x - y)/y
This manipulation shows us that the time it takes to fill tank 1 is definitely shorter than the time it takes to fill tank 2.
(2) INSUFFICIENT: We can express this statement algebraically as: 1/2(z) > 2(x - y). We cannot use this expression to provide us meaningful information about the question.
The correct answer is A.
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