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

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Manager
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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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55% (02:09) correct 45% (02:22) wrong based on 578 sessions

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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jul 2013, 14:04, edited 1 time in total.
Edited the question.

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Re: DS - Tank [#permalink]

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23 Jan 2008, 12:33
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Expert's post
it seems to be A.
What is a source of question?
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Re: DS - Tank [#permalink]

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23 Jan 2008, 12:52
Hi Walker,

The source is ManhattanGmat
Cuold you please detail a little how you reached the answer?

Thanks

walker wrote:
it seems to be A.
What is a source of question?

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Re: DS - Tank [#permalink]

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23 Jan 2008, 13:29
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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

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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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14 Mar 2011, 01:15
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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"
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14 Mar 2011, 04:07
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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: DS Work Rate Problems [#permalink]

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02 Oct 2011, 00:51
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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.
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Re: Reserve tank 1 is capable of holding z galllons of water [#permalink]

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16 Dec 2011, 07:00
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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. Wat [#permalink]

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21 Jan 2014, 11:35
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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
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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
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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 $$\frac{2(x-y)}{y}$$

$$\frac{z}{x-y}$$ ... $$\frac{2(x-y)}{y}$$
$$yz$$ ... $$2(x-y)(x-y)$$
$$yz$$ ... $$2x^2-4xy+2y^2$$

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.

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.

+1 Kudos if you like the post

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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.

Therefore, Only A is sufficient.

Hope this helps.

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Re: Reserve tank 1 is capable of holding z gallons of water. Wat   [#permalink] 20 Jul 2017, 09:29
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# Reserve tank 1 is capable of holding z gallons of water. Wat

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