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Reserve tank 1 is capable of holding z gallons of water. Water is pump
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Updated on: 05 Apr 2018, 05:42
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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 (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) \(zy < 2x^24xy+2y^2\) (2) Total capacity of tank 2 is less than one half that of tank 1.
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Originally posted by JCLEONES on 23 Jan 2008, 12:18.
Last edited by Bunuel on 05 Apr 2018, 05:42, edited 2 times in total.
Edited the question.




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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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14 Mar 2011, 01:15
Time to fill tank 1= z/(xy) Tank 1 will be (xy) full after 1 minute Thus, capacity of "tank 2"=2(xy) Time to fill "tank 2"=2(xy)/y Q: is z/(xy) < 2(xy)/y OR is zy< 2 (xy)^2 1. zy<2x^24xy+2y^2 zy< 2(x^22xy+y^2) zy< 2(xy)^2 Sufficient. 2. 2(xy) < (1/2)z 4 < z/(xy) z/(xy) > 4 But is; z/(xy) < 2(xy)/y Can't simplify any further. Not sufficient. Ans: "A"
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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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23 Jan 2008, 13:29
capacity of tank 2 is u = 2*(xy)
time it takes for tank 2 to get filled is 2*(xy)/y time it takes for tank 1 to get filled is z/(xy)
z/(xy)  2*(xy)/y < 0? equivalent (since y > 0 , xy > 0)
zy < 2*(xy)^2 = 2*x^24*x*y + 2*y^2 (1) is sufficient 2 is irrelevant



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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14 Mar 2011, 00:44
I'd say A.
1 tells us that if Z was 100, x and y were 10 and 5 respectively, 1 would not be true. for 1 to be true, x and y will be 10 and 1 or around that area.
B tells us nothing about the rate at which water is flowing into the second tank.
Any other thoughts?



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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14 Mar 2011, 04:07
Another "lone wolf". Here the complex equation is A Quote: # The Lone Wolf
A lone wolf question almost always has a free standing number(or numbers), and a more complex looking equation as the other option. For e.g.
"On a loan, evil necromonger charges X% interest in the first year, and Y% interest in the second. If he loaned Rhyme 20,000$ in 2006, how much Rhyme pay by interest in 2008?" A) X = 10 B) (X + Y + XY/100) = 100
You can almost be certain, that in such questions, your equations to the stem will reduce to a form that looks like (B), so (A) is actually redundant. Be careful of lone wolves because they will bite you in the posterior if you choose (C).
If you notice a lone wolf question, and you have no clue on how to solve the problem, choose (B) (or whichever is the complex equation).



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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02 Oct 2011, 00:51
After one minute there is \(y\) gallons in the tank 2, so the capacity of the tank 2 is \(2(xy)\) gallons. Obviously, each minute the tank 1 is filled with \(xy\) 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: \(A(xy)=z\) \(By=2(xy)\) \(A=\frac{z}{xy}\) \(B=\frac{2(xy)}{y}\) We need to compare A and B, so we are comparing \(\frac{z}{xy}\) and \(\frac{2(xy)}{y}\) \(\frac{z}{xy}\) ... \(\frac{2(xy)}{y}\) \(yz\) ... \(2(xy)(xy)\) \(yz\) ... \(2x^24xy+2y^2\) If (1) is true, then \(yz< 2x^24xyy^2\) Since \(2x^24xy+2y^2> 2x^24xyy^2\), then \(yz <2x^24xy+2y^2\) and we are able to compare two time periods. The statement (1) alone is susfficient. If (2) is true, then \(2(xy)<0.5z\) \(\frac{z}{xy}>4\) This means that \(A>4\) However, \(B=\frac{2(xy)}{y}\), so there is no z and we only know that \(x>y\), but nothing could be said to compare \(xy\) 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.
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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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16 Dec 2011, 07:00
Nice problem. Got to the answer but took more than 3 mins... Problem statement itself took very long to read and understand
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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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10 Dec 2016, 08:41
bagrettin wrote: After one minute there is \(y\) gallons in the tank 2, so the capacity of the tank 2 is \(2(xy)\) gallons. Obviously, each minute the tank 1 is filled with \(xy\) 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: \(A(xy)=z\) \(By=2(xy)\)
\(A=\frac{z}{xy}\) \(B=\frac{2(xy)}{y}\)
We need to compare A and B, so we are comparing \(\frac{z}{xy}\) and \(\frac{2(xy)}{y}\)
\(\frac{z}{xy}\) ... \(\frac{2(xy)}{y}\) \(yz\) ... \(2(xy)(xy)\) \(yz\) ... \(2x^24xy+2y^2\)
If (1) is true, then \(yz< 2x^24xyy^2\) Since \(2x^24xy+2y^2> 2x^24xyy^2\), then \(yz <2x^24xy+2y^2\) and we are able to compare two time periods. The statement (1) alone is susfficient.
If (2) is true, then \(2(xy)<0.5z\) \(\frac{z}{xy}>4\) This means that \(A>4\) However, \(B=\frac{2(xy)}{y}\), so there is no z and we only know that \(x>y\), but nothing could be said to compare \(xy\) 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. I did not get why did you use yz< 2x^24xyy^2 in the above solution. The solution is sufficient without the usage of this equation. +1 Kudos if you like the post



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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20 Jul 2017, 09:29
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 (XY) G/M Z Gallons would get filled in Z/(XY) Capacity of T2 = 2(XY) G/M T2 water is being filled at Y G/M Therefore, T2 would get filled = 2(XY)/Y A) 2 (XY)^2 > ZY => 2(XY)/Y > Z/(XY) 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.



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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05 Apr 2018, 04:34
HOW DO WE SOLVE SUCH QUES IN 2 MIN . IT TOOK ME MORE THAN 2 MIN TO UNDERSTAND AND SOLVE THE SAME.CAN SOME PLS SUGGEST ME WITH HIS OR HER APPROACH



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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01 May 2018, 05:59
Bunuel  Please can you help suggest if is there any method in which we can approach to solve in 2 mins ?? Thanks in advance



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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16 Dec 2018, 09:49
What is the difficulty level of this question.



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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16 Dec 2018, 16:02
JCLEONES 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 (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) \(zy < 2x^24xy+2y^2\)
(2) Total capacity of tank 2 is less than one half that of tank 1. Dear GMATGuruNYCan you share your thoughts on this question? Thanks in advance



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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18 Dec 2018, 11:36
Mo2men wrote: JCLEONES 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 (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) \(zy < 2x^24xy+2y^2\)
(2) Total capacity of tank 2 is less than one half that of tank 1. Dear GMATGuruNYCan you share your thoughts on this question? Thanks in advance 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 = 102 = 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 onehalf 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.
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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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16 Aug 2019, 14:53
JCLEONES 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 (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) \(zy < 2x^24xy+2y^2\)
(2) Total capacity of tank 2 is less than one half that of tank 1. Do we have any other approach to this question GMATinsightVeritasKarishma



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Re: Reserve tank 1 is capable of holding z gallons of water. Water is pump
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29 Aug 2019, 11:12
I manage to get this problem correct by pluging numbers, can someone please try to explain me differently with algebra ? I don't really understand the solutions above



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Reserve tank 1 is capable of holding z gallons of water. Water is pump
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29 Aug 2019, 12:17
JCLEONES 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 (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) \(zy < 2x^24xy+2y^2\)
(2) Total capacity of tank 2 is less than one half that of tank 1. 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 = xy. Since the zgallon tank is filled at a net rate of xy gallons per minute, we get: Time fill tank 1 \(= \frac{capacity}{rate} = \frac{z}{xy}\) 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) = (xy)(1) = xy. Since the capacity of tank 2 is twice this number of gallons, we get: Capacity of tank 2 = 2(xy) = 2x2y. 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 \(\frac{z}{xy}< \frac{2x2y}{y}\)? Simplifying the question stem, we get: \(zy < (2x2y)(xy)\) \(zy < 2x^24xy+2y^2\) Question stem, rephrased: Is \(zy < 2x^24xy+2y^2\)? Statement 1: \(zy < 2x^24xy+2y^2\) The answer to the rephrased question stem is YES. SUFFICIENT. Statement 2: Since the capacity of tank 2 = 2x2y and the capacity of tank 1 = z, we get: \(2x2y < \frac{1}{2}z\) \(4x4y < z\) \(4 > \frac{z}{xy}\) \(\frac{z}{xy} < 4\) No way to answer the original question stem or the rephrased question stem. INSUFFICIENT.
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