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Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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23 Jan 2008, 12:18

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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^2-4xy+2y^2 (2) Total capacity of tank 2 is less than one half that of tank 1.

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).

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 \(\frac{2(x-y)}{y}\)

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.
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Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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21 Jan 2014, 11:35

Hello from the GMAT Club BumpBot!

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Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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29 Jun 2015, 10:12

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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11 Aug 2016, 06:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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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 \(2(x-y)\) 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 \(\frac{2(x-y)}{y}\)

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.

I did not get why did you use yz< 2x^2-4xy-y^2 in the above solution. The solution is sufficient without the usage of this equation.

Re: Reserve tank 1 is capable of holding z gallons of water. Wat [#permalink]

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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 (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.

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