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A certain pump working at a constant rate is used to remove rain water

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A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 14 Mar 2020, 18:35
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GMATBusters’ Quant Quiz Question -8



A certain pump working at a constant rate is used to remove rain water from a basement during a rainstorm. If water is entering the basement at a constant fate and the pump is turned on exactly when water begins flooding the basement, is more than 1/2 of the basement flooded with water after 3 hours?

1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.
2) After 2 hours, the basement is 2/5 flooded with water.

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A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 14 Mar 2020, 18:35
Two pumps are working together, need to find whether the tank be filled more than 50% after 3 hours


Statement 1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.

Neither we can find the individual rate now we have the size of the basement.

NOT sufficient.


Statement 2) After 2 hours, the basement is 2/5 flooded with water.

After 2 hours, the basement is 40% flooded with water. So we know that every 1 hours, the tank is flooded with 20% with water. So after 3 hours we will have 60% tank flooded with water at this same rate.

Hence, Sufficient.


Answer B
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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 14 Mar 2020, 20:03
A certain pump working at a constant rate is used to remove rain water from a basement during a rainstorm. If water is entering the basement at a constant fate and the pump is turned on exactly when water begins flooding the basement, is more than 1/2 of the basement flooded with water after 3 hours?

Rate of Inflow = X/hr, Rate of outflow = Y/hr

1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.
Let's assume, X= 6 and Y = 1, Total net amount of water shall be remained in basement after 1 hr = 5,
Total net amount of water shall be remained in basement after 2 hr = 5+6-1=10,
Total net amount of water shall be remained in basement after 3 hr = 10+6-1=15
However, we don't know the exact volume of the basement. So, insufficient.

2) After 2 hours, the basement is 2/5 flooded with water. Insufficient as we don't know rate of inflow and outflow of water in the basement.

1) + 2) Based on above assumption,
Total net amount of water shall be remained in basement after 2 hr = 10, which is 2/5th of total. So, total = 25.
Total net amount of water shall be remained in basement after 3 hr = 15, which is more than 50% of 25. So, sufficient.

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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 14 Mar 2020, 20:20
The Pump draining the tank and pump filling the tank is opened at the same time

Need: Is more than 1/2 of the basement flooded with water after 3 hours?

1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.

We do not have the exact rate of each pump. This option is Insufficient.

2) After 2 hours, the basement is 2/5 flooded with water.

After 2 hours, the basement is 40% flooded with water. So we know that every 1 hours, the tank is flooded with 20% with water. So after 3 hours we will have 60% tank flooded with water at this same rate. So Option B is sufficient.

Ans: B
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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 14 Mar 2020, 21:28
OA is C
Statement 1: water is flowing in at rate of 6times then it's pumping out.
So for first hour it will fill
6X-X water=5x
Second Hour : 12x-2x=10x
Third hour=18x-3x=15x
And so on (insufficient)
Statement 2: basement is 2/5 filled in 2 hours. But we don't know the rate at which water is filling in the basement.
(Insufficient)

Taking both statements, the water is filling 6x-x in 1 hour so he is filling 10x in 2 hours (12x-2x)
That gives 15x in 3 hours which is half of 30x at which the water would have filled in basement without water outlet.
(Sufficient)
So OA is C

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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 15 Mar 2020, 02:44
Given: A certain pump working at a constant rate is used to remove rain water from a basement during a rainstorm.

Asked: If water is entering the basement at a constant rate and the pump is turned on exactly when water begins flooding the basement, is more than 1/2 of the basement flooded with water after 3 hours?

1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.
Let the rate of pump pushing water out of the basement be x litres/hour
Rate of water entering the basement = 6x litres /hour
Rate of basement flooding = 5x litres/hour
Basement filled after 3 hours = 15x litres
Is 15x > 1/2 * Basement capacity in litres
Since x and basement capacity are unknown
NOT SUFFICIENT

2) After 2 hours, the basement is 2/5 flooded with water.
Since water is entering the basement at a constant rate and the pump is turned on exactly when water begins flooding the basement and after 2 hours, the basement is 2/5 flooded with water, rate of water entering the basement > rate of pump pushing water out of basement
In 2 hours, basement is 2/5 flooded with water
In 3 hours, basement will be 3/5 > 1/2 flooded with water
SUFFICIENT

IMO B
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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 15 Mar 2020, 04:21
Answer :B
Stat:1
Water entry rate=6X water pumping rate
No information about flooding
Not sufficient
Stat:2
(water entry rate-water pumping rate)X2= 2/5 V ,V stands for capacity of basement for flooding.
Our requirement is :Is basement flooded more than V/2 after 3 hrs ie (water entry rate-water pumping rate)X 3>V/2
from statement 2,we can answer definitely
Sufficient
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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 15 Mar 2020, 05:06
Statement 1: We don't know size of the basement.
Insufficient

Statement 2: Let rate of pump be x and rate at which water is flooding the basement be y
In 2 hrs, 2/5th basement is flooded.
Work = Rate x time
\(\frac{2}{5}\) = 2y
y = 1/5
In 3 hrs, basement flooded = rate x time = \(\frac{1}{5}\) * 3
\(\frac{3}{5}\)th basement will be flooded.

But we don't know the relation between x and y.
Insufficient.

Statement 1 & 2: y = 6x
Rate of pump = y/6 = 1/30
Work done by pump for removing water in 3hrs
= 3 * \(\frac{1}{30}\)
=\(\frac{1}{10}\)

So after 3hrs, portion of basement flooded = \(\frac{3}{5}\) - \(\frac{1}{10}\)
=\(\frac{5}{10}\)
=\(\frac{1}{2}\)

Sufficient

Answer: C
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Re: A certain pump working at a constant rate is used to remove rain water  [#permalink]

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New post 15 Mar 2020, 06:34
Quote:
A certain pump working at a constant rate is used to remove rain water from a basement during a rainstorm. If water is entering the basement at a constant fate and the pump is turned on exactly when water begins flooding the basement, is more than 1/2 of the basement flooded with water after 3 hours?

1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.
2) After 2 hours, the basement is 2/5 flooded with water.


Statement 1: Inflow = 6 Outflow = -1

Since we don't know the capacity of the tank we cannot calculate whether the tank will be more than half empty after 3 hours.

2) After 2 hours, the basement is 2/5 flooded with water.

Since we know this, we can infer than every hour the basement is getting flooded 1/5th. So in 2 hours it will be 2/5 and in 3 hours it will be 3/5 which is more than 1/2. Sufficient.

Answer B
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Re: A certain pump working at a constant rate is used to remove rain water   [#permalink] 15 Mar 2020, 06:34

A certain pump working at a constant rate is used to remove rain water

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