GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2019, 13:52 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # A right circular cone, twice as tall as it is wide at its

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 29 Sep 2009
Posts: 16
A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

5
30 00:00

Difficulty:   95% (hard)

Question Stats: 34% (02:26) correct 66% (02:33) wrong based on 567 sessions

### HideShow timer Statistics

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area.
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

9
7
jax91 wrote:
(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D)
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means? H - height of cone, R radius of cone.
h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area. Top surface area of water = $$9\pi=\pi*r^2$$ --> $$r=3$$ --> $$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$ --> $$h=12$$ --> $$V=\frac{1}{3}*\pi*r^2*h=36*\pi$$ cubic centimeters.

Leak rate 2 cubic centimeters per hour --> $$time=\frac{36\pi}{2}$$ hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

Attachment: Untitled.png [ 17.59 KiB | Viewed 10213 times ]

_________________
##### General Discussion
Manager  Joined: 02 Jan 2009
Posts: 76
Location: India
Schools: LBS
Re: Leak of water from the cone  [#permalink]

### Show Tags

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D)
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.
_________________
The Legion dies, it does not surrender.
Intern  Joined: 27 Jun 2011
Posts: 1
Re: Leak of water from the cone  [#permalink]

### Show Tags

1
It cant be A cause the question says, e cone is partially filled with water.

A can be true only when the cone is fully filled.
Intern  Joined: 29 Jun 2011
Posts: 11
Location: Ireland
Re: Leak of water from the cone  [#permalink]

### Show Tags

1
svikram wrote:
It cant be A cause the question says, e cone is partially filled with water.

A can be true only when the cone is fully filled.

If we know the ratio for height:width for any volume in a cone, then that ratio applies to all volumes. This rule is due to the fact that the angles in the cone stay constant when the volume changes. Statement 1 gives us the area at the top of the water. This allows us to find the water volume, using the height:width ratio provided, and subsequently the rate of leaking. A is the answer.
_________________
http://www.testprepdublin.com

For the best GMAT, GRE, and SAT preparation.
Manager  Joined: 27 Dec 2011
Posts: 54
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!
Manager  Joined: 04 Apr 2013
Posts: 117
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

kartik222 wrote:
hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!

kartik,

similar triangle property...

R/H = r/h

since 2R=H

r/h = 1/2

so h = 6.
_________________
Maadhu

MGMAT1 - 540 ( Trying to improve )
Manager  B
Status: Student
Joined: 26 Aug 2013
Posts: 171
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32 GPA: 3.44
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

Hi,

have a small question: it is stated that "The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour"

It has been said that : the leak rate 2 cubic centimeters per hour --> 36pi/2. Meaning that it will take 18pi hours to fill the cone.

But, the cone could be half full. or 3/4 full. We don't know!

Therefore, the result will be different since they ask : "how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means"

It could be 18pi/2 or 18pi/4!

Where did i miss something? Plz explain!

Thanks!
_________________
Think outside the box
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

Paris75 wrote:
Hi,

have a small question: it is stated that "The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour"

It has been said that : the leak rate 2 cubic centimeters per hour --> 36pi/2. Meaning that it will take 18pi hours to fill the cone.

But, the cone could be half full. or 3/4 full. We don't know!

Therefore, the result will be different since they ask : "how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means"

It could be 18pi/2 or 18pi/4!

Where did i miss something? Plz explain!

Thanks!

$$36\pi$$ is the volume of water in the cone not the total volume of the cone.
_________________
Manager  Joined: 26 Sep 2013
Posts: 189
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: Leak of water from the cone  [#permalink]

### Show Tags

Bunuel wrote:
jax91 wrote:
(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D)
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?
Attachment:
Untitled.png
H - height of cone, R radius of cone.
h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area. Top surface area of water = $$9\pi=\pi*r^2$$ --> $$r=3$$ --> $$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$ --> $$h=12$$ --> $$V=\frac{1}{3}*\pi*r^2*h=36*\pi$$ cubic centimeters.

Leak rate 2 cubic centimeters per hour --> $$time=\frac{36\pi}{2}$$ hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area. Top surface area of water = $$9\pi=\pi*r^2$$ --> $$r=3$$ --> $$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$

after you solved for r=3, how did you get

$$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$

Aren't R, H, and h, all unknown?
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: Leak of water from the cone  [#permalink]

### Show Tags

AccipiterQ wrote:
Bunuel wrote:
jax91 wrote:
(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D)
(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?
Attachment:
Untitled.png
H - height of cone, R radius of cone.
h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area. Top surface area of water = $$9\pi=\pi*r^2$$ --> $$r=3$$ --> $$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$ --> $$h=12$$ --> $$V=\frac{1}{3}*\pi*r^2*h=36*\pi$$ cubic centimeters.

Leak rate 2 cubic centimeters per hour --> $$time=\frac{36\pi}{2}$$ hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

The top surface of the water in the cone is currently $$9\pi$$ square centimeters in area. Top surface area of water = $$9\pi=\pi*r^2$$ --> $$r=3$$ --> $$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$

after you solved for r=3, how did you get

$$\frac{R}{H}=\frac{r}{h}=\frac{1}{4}$$

Aren't R, H, and h, all unknown?

We are given that the cone, twice as tall as it is wide, which means that H = 2D --> H = 4R --> R/H = 1/4. Because of similar triangles, the same applies to r and h.

Hope it's clear.
_________________
Intern  Joined: 02 Dec 2013
Posts: 7
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

maaadhu wrote:
kartik222 wrote:
hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!

kartik,

similar triangle property...

R/H = r/h

since 2R=H

r/h = 1/2

so h = 6.

I really find these problems very tough. Is there any reference to these problems ???
Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 274
A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

maaadhu wrote:
kartik222 wrote:
hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!

kartik,

similar triangle property...

R/H = r/h

since 2R=H

r/h = 1/2

so h = 6.

hi

how can you deduce that 2R = H

the cone is twice as tall as it is wide at its greatest width, so

H = 2 x 2R = 4R, which implies

R / 4R = r / h = 1/4, and since, r = 3, h= 12

Isn't that ?

thanks
Manager  S
Joined: 29 Dec 2018
Posts: 80
Location: India
WE: Marketing (Real Estate)
Re: A right circular cone, twice as tall as it is wide at its  [#permalink]

### Show Tags

erictwendell wrote:
maaadhu wrote:
kartik222 wrote:
hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!

kartik,

similar triangle property...

R/H = r/h

since 2R=H

r/h = 1/2

so h = 6.

I really find these problems very tough. Is there any reference to these problems ???

I recommend you to study the basics of 3D Geometries chapter

You can find the link of this from the GMAT Club Math book by bb & Bunuel here https://gmatclub.com/forum/math-3-d-geo ... ml#p792331
_________________
Keep your eyes on the prize: 750 Re: A right circular cone, twice as tall as it is wide at its   [#permalink] 04 Aug 2019, 09:55
Display posts from previous: Sort by

# A right circular cone, twice as tall as it is wide at its

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  