Reserve tank 1 is capable of holding z gallons of water. Water is pump

Question

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 (x > y).The water that leaks out of tank 1 drips into tank 2,which also starts off empty. If the total capacity of tank 2 is twice the number of gallons that remains in tank 1 after 1 minute, does tank 1 fill up before tank 2?

(1) \(zy < 2x^2-4xy+2y^2\)

(2) Total capacity of tank 2 is less than one half that of tank 1.

(1)  zy < 2x^2-4xy+2y^2

(2) Total capacity of tank 2 is less than one half that of tank 1.

fluke · Accepted Answer

Time to fill tank 1= z/(x-y)
Tank 1 will be (x-y) full after 1 minute
Thus, capacity of "tank 2"=2(x-y)
Time to fill "tank 2"=2(x-y)/y

Q: is z/(x-y) < 2(x-y)/y
OR
is zy< 2 (x-y)^2

1. zy<2x^2-4xy+2y^2
zy< 2(x^2-2xy+y^2)
zy< 2(x-y)^2
Sufficient.

2. 2(x-y) < (1/2)z
4 < z/(x-y)
z/(x-y) > 4
But is;
z/(x-y) < 2(x-y)/y
Can't simplify any further.
Not sufficient.

Ans: "A"

bagrettin · Answer

After one minute there is y gallons in the tank 2, so the capacity of the tank 2 is 2(x-y) gallons. Obviously, each minute the tank 1 is filled with x-y gallons of water, and tank 2 is filled with y gallons. Let A is the number of minutes after which the 1 tank is full, and B is the number of minutes after which 2 the 2 tank is full. Then: A(x-y)=z By=2(x-y) A=\frac{z}{x-y} B=\frac{2(x-y)}{y} We need to compare A and B, so we are comparing \frac{z}{x-y} and \frac{2(x-y)}{y} \frac{z}{x-y} ... \frac{2(x-y)}{y} yz ... 2(x-y)(x-y) yz ... 2x^2-4xy+2y^2 If (1) is true, then yz< 2x^2-4xy-y^2 Since 2x^2-4xy+2y^2> 2x^2-4xy-y^2 , then yz <2x^2-4xy+2y^2 and we are able to compare two time periods. The statement (1) alone is susfficient. If (2) is true, then 2(x-y)<0.5z \frac{z}{x-y}>4 This means that A>4 However, B=\frac{2(x-y)}{y} , so there is no z and we only know that x>y , but nothing could be said to compare x-y and y . For example, if x=2y , then B=2 and A>B . However, if x=5y , then B=8 and we could not compare A and B. So, the answer is (A) NOTE: You should post DS problems in the other forum.

maratikus · Answer

capacity of tank 2 is u = 2*(x-y)

time it takes for tank 2 to get filled is 2*(x-y)/y
time it takes for tank 1 to get filled is z/(x-y)

z/(x-y) - 2*(x-y)/y < 0? equivalent (since y > 0 , x-y > 0)

zy < 2*(x-y)^2 = 2*x^2-4*x*y + 2*y^2 (1) is sufficient
2 is irrelevant

Kavya123 · Answer

T1 - Water is being filled at the rate of X Gallons/Minute and leaking at the rate of Y G/M
In one minute T1 is getting filled at (X-Y) G/M
Z Gallons would get filled in Z/(X-Y)

Capacity of T2 = 2(X-Y) G/M
T2 water is being filled at Y G/M
Therefore, T2 would get filled = 2(X-Y)/Y

A) 2 (X-Y)^2 > ZY
=> 2(X-Y)/Y > Z/(X-Y)
Therefore A is sufficient

B) The total capacity of tank 2 is less than one half that of Tank 1
This doesn't specify the relationship between the rates at which the tanks are being filled. Only the relationship between the capacities.

Therefore, Only A is sufficient.

Hope this helps.
:-D

GMATGuruNY · Answer

Statement 1: zy < 2x2 - 4xy + 2y2  
To see the implications of this inequality, plug in values for x and y and solve for z. 
Let x=10 and y=2. 
Then: 
z(2) < 2(102) - 4(10)(2) + 2(22) 
2z < 128 
z < 64. 
Here, the capacity of tank 1 is LESS than 64 gallons.

Tank 1: 
Since tank 1 receives x=10 gallons per minute and loses y=2 gallons per minute, the net gain for tank 1 = 10-2 = 8 gallons per minute. 
Since the capacity of tank 1 is LESS than 64 gallons, the time to fill tank 1 at a rate of 8 gallons per minute must be LESS than 64/8 = 8 minutes.

Tank 2: 
After one minute, the volume in tank 1 = 8 gallons. 
Since the capacity of tank 2 is twice the volume in tank 1 after one minute, the capacity of tank 2 = 2*8 = 16 gallons. 
Time to fill tank 2 at a rate of y=2 gallons per minute = 16/2 = 8 minutes.

While tank 1 requires LESS than 8 minutes, tank 2 requires EXACTLY 8 minutes.
The case above illustrates that tank 1 will fill up before tank 2. 
SUFFICIENT.

Statement 2: The total capacity of tank 2 is less than one-half that of tank 1.  
In statement 1 above, it is possible that the capacity of tank 2 = 16 gallons, while the capacity of tank 1 = 63 gallons. 
These values also satisfy statement 2. 
As we saw above, the result will be that tank 1 fills up before tank 2. 
But if we increase the capacity of tank 1 to 1000 gallons and leave all of the other values the same, tank 2 will fill up before tank 1. 
INSUFFICIENT.

A

GMATGuruNY · Answer

Tank 1:
Since water is PUMPED IN at x gallons per minute but LEAKS OUT at y gallons per minute, the net gain per minute = x-y.
Since the z-gallon tank is filled at a net rate of x-y gallons per minute, we get:
Time fill tank 1  = \frac{capacity}{rate} = \frac{z}{x-y}

Tank 2:
 The total capacity of tank 2 is twice the number of gallons that remains in tank 1 after 1 minute. 
After 1 minute, the number of gallons in tank 1 = (net gain per minute)(one minute) = (x-y)(1) = x-y.
Since the capacity of tank 2 is twice this number of gallons, we get:
Capacity of tank 2 = 2(x-y) = 2x-2y.

The water that leaks out of tank 1 drips into tank 2 .
Since water leaks from tank 1 into tank 2 at a rate of y gallons per minute, we get:
Time to fill tank 2  = \frac{capacity}{rate} = \frac{2x - 2y}{y}

Does tank 1 fill up before tank 2? 
In other words:
 Is the time fill tank 1 less than the time to fill tank 2? 
Original question stem:
Is  \frac{z}{x-y}< \frac{2x-2y}{y} ?

Simplifying the question stem, we get:
 zy < (2x-2y)(x-y) 
 zy < 2x^2-4xy+2y^2

Question stem, rephrased:
Is  zy < 2x^2-4xy+2y^2 ?

Statement 1:  zy < 2x^2-4xy+2y^2 
The answer to the rephrased question stem is YES.
SUFFICIENT.

Statement 2:
Since the capacity of tank 2 = 2x-2y and the capacity of tank 1 = z, we get:
 2x-2y < \frac{1}{2}z 
 4x-4y < z 
 4 > \frac{z}{x-y} 
 \frac{z}{x-y} < 4 
No way to answer the original question stem or the rephrased question stem.
INSUFFICIENT.

A

GMATinsight · Answer

Please find the solution as depicted in figure

Answer: Option A

sujoykrdatta · Answer

Capacity of tank 1 = z gallons ... (i) Effective filling rate of tank 1 = (x - y) gallons/min => Time taken to fill tank 1 = \frac{z}{(x-y)} minutes ... (ii) Volume of water in tank 1 after 1 minute = (x - y) gallons => Volume of tank 2 = 2(x - y) gallons ... (iii) Filling rate of tank 2 = y gallons/min => Time taken to fill tank 2 = \frac{2(x - y)}{y} minutes ... (iv) We need to verify if: tank 1 fills up before tank 2 i.e. if \frac{z}{(x-y)} < \frac{2(x - y)}{y} i.e. if yz < 2(x - y)^2 i.e. if yz < 2x^2 - 4xy + 2y^2 ... (v) From statement 1: The exact condition in (iii) above is mentioned in this statement --- Sufficient From statement 2: Capacity of tank 2 is less than one half that of tank 1 => 2(x - y) < z/2 => z > 4(x - y) However, this is not enough to verify condition (v) above - Insufficient Answer A

Dhwanii · Answer

Statement 2 - Capacity of tank 2 is less than one half that of tank 1

2(x−y)<z/2, over here why are we saying Capacity of tank 2 is 2(x-y) as that's not the overall capacity but the capacity after 1 min. How do we infer that total capacity of tank 2 will follow the same equation as after 1 min

RishabhChowdhury · Answer

I have a doubt here. The solution make sense, but the reason I was unable to solve this question was because of a language/interpretation error. When it says that the capacity of Tank 2 is twice the number of gallons remaining in Tank 1, I thought it meant twice the number of gallons remaining to be filled, i.e. z-(x-y). I believe the question statement would have made much more sense if it simply said twice the number of gallons in Tank 1 after 1 min.

Could someone help me understand whether this was a deliberate trap? Or did I miss something?
If this could be a trap, how do I not miss things like this in the future? It would be very helpful if someone could help me understand through this example.

vishnubansal1812 · Answer

While I understand the 1st equation, and have arrived on the second equation [ 4(x - y) < z ]. My approach further:

4 (x - y) * y < zy
=> 4xy - 4y^2 < zy
=> 2y^2 + 2y^2 - 4xy > zy [EDIT: This is wrong. The correct equation would be 2y^2 + 2y^2 - 4xy > -zy, which is an insufficient condition. Thus A]
Since x > y, 2y^2 + 2x^2 - 4xy > zy which is the same as the first equation. Therefore my answer was D.

Reserve tank 1 is capable of holding z gallons of water. Water is pump

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Reserve tank 1 is capable of holding z gallons of water. Water is pump

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