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# M07-26

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:35
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Difficulty:

35% (medium)

Question Stats:

67% (01:10) correct 33% (01:00) wrong based on 67 sessions

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A right circular cylinder of 72 cubic meters is completely filled with water. If water evaporates from the cylinder at a constant rate of two liters per hour per one square meter of surface, how long will it take for 30 liters of water to evaporate?

(1) The height of the cylinder is 2 meters.

(2) The radius of the base of the cylinder is $$\frac{6}{\sqrt{\pi}}$$ meters.

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15 Sep 2014, 23:35
Official Solution:

A right circular cylinder of 72 cubic meters is completely filled with water. If water evaporates from the cylinder at a constant rate of two liters per hour per one square meter of surface, how long will it take for 30 liters of water to evaporate?

To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. So, basically all we need is ether the area of the surface or the height of the cylinder.

(1) The height of the cylinder is 2 meters. Sufficient.

(2) The radius of the base of the cylinder is $$\frac{6}{\sqrt{\pi}}$$ meters. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

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19 Sep 2014, 01:32
1
I am unable to understand the logic behind 30/(area/2).

As per my understanding, There are two circular bases of a cylinder since we are looking at one (from where water evaporates) so Area/2.

Combining these entities ALL together seems like a problem here.

Concepts that involve three dependent quantities tend to be always tricky like 2 litre PER hour PER one square meter of surface.

How to get a hang of such questions?
Math Expert
Joined: 02 Sep 2009
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19 Sep 2014, 07:49
1
earnit wrote:
I am unable to understand the logic behind 30/(area/2).

As per my understanding, There are two circular bases of a cylinder since we are looking at one (from where water evaporates) so Area/2.

Combining these entities ALL together seems like a problem here.

Concepts that involve three dependent quantities tend to be always tricky like 2 litre PER hour PER one square meter of surface.

How to get a hang of such questions?

There was a formatting error. Edited.

Water evaporates from the top of a pool, which is open. We are told that 2 liters evaporate from each square meter of surface per 1 hour.

So, to find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: $$2*area$$ will be the amount of water that evaporates each hour, thus $$time=\frac{30}{2*area}$$.

For example if the surface area of the top is 5m^2, then in one hour 5*2=10 liters of water evaporates hence it'll take 30/10=3 hours 30 liters of water to evaporate.
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19 Sep 2014, 08:22
1
Bunuel wrote:
earnit wrote:
I am unable to understand the logic behind 30/(area/2).

As per my understanding, There are two circular bases of a cylinder since we are looking at one (from where water evaporates) so Area/2.

Combining these entities ALL together seems like a problem here.

Concepts that involve three dependent quantities tend to be always tricky like 2 litre PER hour PER one square meter of surface.

How to get a hang of such questions?

There was a formatting error. Edited.

Water evaporates from the top of a pool, which is open. We are told that 2 liters evaporate from each square meter of surface per 1 hour.

So, to find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: $$2*area$$ will be the amount of water that evaporates each hour, thus $$time=\frac{30}{2*area}$$.

For example if the surface area of the top is 5m^2, then in one hour 5*2=10 liters of water evaporates hence it'll take 30/10=3 hours 30 liters of water to evaporate.

So as per my understanding i will further elaborate the explanation.
The key takeaway from this Question is managing three dependent entities, taking two at a time.

2 liters evaporate from each square meter (PER square meter) of surface PER hour.

One look at it seems like a three way battle but here's how it was broken down.

Quantity that Evaporate ---- Surface Area (top)
2 Liters ---- 1 m^2
? ---- Surface Area of Cylinder (top)

So, 2*Surface Area of Cylinder = 2*area is the quantity that evaporates in 1 hour.

Now, 2* area is the quantity that evaporates in 1 hour
so, 30 liters will take =[30/(2*area)] hours

Hence, a connecting flow from Quantity to Area to finally time.
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17 Dec 2014, 13:51
Did I set up this equation correctly? "two liters per hour per one square meter of surface" = $$\frac{2L}{(h)(m^2)}$$
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Joined: 19 Sep 2014
Posts: 22
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16 Aug 2015, 07:04
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Please explain the first part of the explanation in detail time=30/(2*area)
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17 Aug 2015, 03:16
1
schak2rhyme wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Please explain the first part of the explanation in detail time=30/(2*area)

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23 Oct 2015, 13:35
pretty simple question, but i was tripped up on deciding whether the water could evaporate if the cylinder were on its side, which i suppose this questions assumes wouldn't be the case.
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Status: GMAT...Not Again.....
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Location: India
Concentration: Strategy, Entrepreneurship
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23 Oct 2015, 22:31
hello bunual,
again thank you for a good tricky que.
i am new to GMATclub, but preparing from 5 months.... and your questions still got me...
i was really fell face down when i got here n solve some of thee que.
great work. kudos to you
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20 Jul 2016, 01:46
Well the question should clearly state that water only evaporates from the top circular face, if its the cylinder is made of clay, water can evaporate from whole surface area..
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Joined: 07 Feb 2016
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GMAT 1: 650 Q47 V34
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13 May 2017, 04:43
shashanksagar wrote:
Well the question should clearly state that water only evaporates from the top circular face, if its the cylinder is made of clay, water can evaporate from whole surface area..

I agree with that. I was also thinking about whether I should only use the top or the whole surface and finally decided for the latter one.
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Joined: 06 Jan 2018
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03 Mar 2018, 00:55
I wondered as well about whether the water could evaporate from all sides somehow (maybe the rate is somehow complex e.g. if you heat up the sides, water will evaporate faster or something, I don't know).

However it doesn't matter as the question is only data sufficiency. If we know the volume + the height OR volume + the radius, we can calculate all relevant facts about the cylinder including the full surface area if necessary, and plug it into the provided evaporation formula.
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15 Jul 2018, 11:19
Bunuel
I did not get why only top surface area of cylinder is needed.
Pls expound.
It will be more helpful if you would solve the required time (just for method understanding if in case this given in PS)
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Re: M07-26 &nbs [#permalink] 15 Jul 2018, 11:19
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# M07-26

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