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

 It is currently 23 May 2019, 22:07 ### 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 cylindrical tank has a base with a circumference of

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

### Hide Tags

Intern  Joined: 21 Jun 2010
Posts: 5
A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

7
33 00:00

Difficulty:   85% (hard)

Question Stats: 61% (02:54) correct 39% (03:03) wrong based on 358 sessions

### HideShow timer Statistics

A cylindrical tank has a base with a circumference of $$4\sqrt{\pi{\sqrt{3}}$$ meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

A. $$\sqrt{2{\sqrt{6}}$$

B. $$\frac{\sqrt{6{\sqrt{6}}}}{2}$$

C. $$\sqrt{2{\sqrt{3}}$$

D. $$\sqrt{3}$$

E. $$2$$

Originally posted by bhushan288 on 28 Nov 2010, 02:04.
Last edited by Bunuel on 09 Jun 2013, 08:33, edited 2 times in total.
Edited the question and added the OA
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: Probability Triangle(700 lvl Qn )  [#permalink]

### Show Tags

6
11
bhushan288 wrote:
hi guys...
can u help me out with this 1....
thnks in advance

A cylindrical tank has a base with a circumference of meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

Hi bhushan288, and welcome to Gmat Club.

Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.
Make sure you type the question in exactly as it was stated from the source.

Also:
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Original question is:

A cylindrical tank has a base with a circumference of $$4\sqrt{\pi{\sqrt{3}}$$ meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

A. $$\sqrt{2{\sqrt{6}}$$

B. $$\frac{\sqrt{6{\sqrt{6}}}}{2}$$

C. $$\sqrt{2{\sqrt{3}}$$

D. $$\sqrt{3}$$

E. $$2$$

Given: $$circumference=4\sqrt{\pi{\sqrt{3}}$$ and $$P(out)=\frac{3}{4}$$

Now, as the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4 then the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base and the triangle itself 1/4 of the are of the base.

Next: $$circumference=4\sqrt{\pi{\sqrt{3}}}=2\pi{r}$$ --> square both sides --> $$16\pi{\sqrt{3}}=4{\pi}^2{r}^2$$ --> $$4{\sqrt{3}}={\pi}{r}^2$$ --> $$area_{base}=\pi{r^2}=4{\sqrt{3}}$$;

The area of the equilateral triangle is 1/4 of the base: $$area_{equilateral}=\frac{1}{4}*4{\sqrt{3}}=\sqrt{3}$$ --> also the ares of the equilateral triangle is $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}$$, where $$a$$ is the length of a side --> $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3}$$ --> $$a=2$$.

Answer: E.
_________________
##### General Discussion
Intern  Joined: 21 Jun 2010
Posts: 5
Re: Probability Triangle(700 lvl Qn )  [#permalink]

### Show Tags

1
Thnks a lot Bunuel...
Manager  Joined: 18 Aug 2010
Posts: 79
Re: Probability Triangle(700 lvl Qn )  [#permalink]

### Show Tags

A cylindrical tank has a base with a circumference of 4(sqrt(pi sqrt(3)) meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

A. $$\sqrt{2{\sqrt{6}}$$

B. $$\frac{\sqrt{6{\sqrt{6}}}}{2}$$

C. $$\sqrt{2{\sqrt{3}}$$

D. $$\sqrt{3}$$

E. $$2$$

Given: $$circumference=4\sqrt{\pi{\sqrt{3}}$$ and $$P(out)=\frac{3}{4}$$

Now, as the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4 then the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base and the triangle itself 1/4 of the are of the base.

Next: $$circumference=4\sqrt{\pi{\sqrt{3}}}=2\pi{r}$$ --> square both sides --> $$16\pi{\sqrt{3}}=4{\pi}^2{r}^2$$ --> $$4{\sqrt{3}}={\pi}{r}^2$$ --> $$area_{base}=\pi{r^2}=4{\sqrt{3}}$$;

The area of the equilateral triangle is 1/4 of the base: $$area_{equilateral}=\frac{1}{4}*4{\sqrt{3}}=\sqrt{3}$$ --> also the ares of the equilateral triangle is $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}$$, where $$a$$ is the length of a side --> $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3}$$ --> $$a=2$$.

Answer: E.[/quote]

Hello Bunuel

ur explanation is perfect . i just cant understand one thing. i know that formula for the side of equilateral triangle inscribed in the circle
should be a= √3 * r where r is radius and a is side of the triangle, but when using this formula i am not getting the right answer in the above exmpl. what could be the problem? is somth. wrong with formula ? thanks
Retired Moderator Joined: 20 Dec 2010
Posts: 1774
Re: Probability Triangle(700 lvl Qn )  [#permalink]

### Show Tags

2
tinki wrote:

Answer: E.

Hello Bunuel

ur explanation is perfect . i just cant understand one thing. i know that formula for the side of equilateral triangle inscribed in the circle
should be a= √3 * r where r is radius and a is side of the triangle, but when using this formula i am not getting the right answer in the above exmpl. what could be the problem? is somth. wrong with formula ? thanks[/quote]

The triangle is not necessarily inscribed because it is not mentioned in the question. It can be any equilateral triangle drawn within the base. The vertices of the triangle may not touch the circle.
_________________
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1391
Location: United States (IN)
Concentration: Strategy, Technology
Re: Probability Triangle(700 lvl Qn )  [#permalink]

### Show Tags

2*pi*r = 4(sqrt(pi sqrt(3))

=> r = 4(sqrt(pi sqrt(3))/2*pi = 2(sqrt(pi sqrt(3))/pi

Area of circle C = pi * r^2 = 4 * pi* 1/(pi)^2 * pi * sqrt(3) = 4*sqrt(3)

A/C = 1/4

=> A = sqrt(3)

Area of Triangle = sqrt(3) = sqrt(3)/4 * (side)^2

So side = sqrt(4) = 2

Answer is E.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Senior Manager  Joined: 23 Oct 2010
Posts: 343
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

could u please explain me why we cant use this formula here ?

The radius of the circumscribed circle is R=a*\sqrt{3}/3

math-triangles-87197.html
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

1
LalaB wrote:
could u please explain me why we cant use this formula here ?

The radius of the circumscribed circle is R=a*\sqrt{3}/3

math-triangles-87197.html

Because we are told that equilateral triangle is painted so not necessarily inscribed on the interior side of the base.
_________________
Intern  Joined: 09 May 2013
Posts: 44
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Hi Bunuel,
can you explain
how can you consider P(out) as fraction of total base?

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

WarriorGmat wrote:
Hi Bunuel,
can you explain
how can you consider P(out) as fraction of total base?

Posted from my mobile device

Bigger the area bigger the probability of a grain landing there. P(out)=3/4 simply means that the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base.
_________________
Intern  Joined: 25 Apr 2013
Posts: 5
Location: India
Concentration: Strategy, Marketing
Schools: INSEAD Jan '15
GPA: 2.7
WE: Information Technology (Computer Software)
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Hi,

Let P(E) = Probability of grain landing inside triangle = 1 - 3/4 = 1/4;--------(1)
Also P(E) = Area of Equilateral Triangle/Area of Base(i.e. Circle) ---------- (2)

Area (Triangle) = (3^1/2 / 4 )*a^2
Area (Circle) = pi*r^2 = pi * (2(3^1/2/pi)^1/2)^2 = 4*3^1/2

By using 1 & 2

a = 4 (Ans.)

Thanks & Regards,
Prateek Sharma
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

pratsh123 wrote:
Hi,

Let P(E) = Probability of grain landing inside triangle = 1 - 3/4 = 1/4;--------(1)
Also P(E) = Area of Equilateral Triangle/Area of Base(i.e. Circle) ---------- (2)

Area (Triangle) = (3^1/2 / 4 )*a^2
Area (Circle) = pi*r^2 = pi * (2(3^1/2/pi)^1/2)^2 = 4*3^1/2

By using 1 & 2

a = 4 (Ans.)

Thanks & Regards,
Prateek Sharma

a=2. Check here: a-cylindrical-tank-has-a-base-with-a-circumference-of-105453.html#p824188
_________________
Manager  Joined: 26 Sep 2013
Posts: 190
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Is there any quicker way to do this one? I started down a similar path and was only about 1/4 done by the time I hit 2 minutes
Intern  Joined: 11 Aug 2013
Posts: 19
Concentration: Strategy
Schools: Foster '16 (II)
GMAT 1: 720 Q47 V42 GPA: 3.47
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Hey guys, I feel like the answer to my problem is something super obvious, but why is the area of the triangle 1/4 of the base (from subtracting the probability 3/4 from 1), resulting in an area of 3.
I got an area of 4, resulting from (Area of Circle)/(Area of Circle + Area of Triangle) = 3/4 (with Area of Circle = 12). I want to say if I was given a problem asking for the probability of red balls when there are 12 red balls and 4 blue balls, i would say the probability is 12/(12+4) = 3/4.

Thank you for the help........I'm slowly losing it with all these fractions, and positives and negatives, and less than greater than's, and that and it not having references, and primary purpase of passages.......
Senior Manager  G
Joined: 03 Apr 2013
Posts: 274
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41 GPA: 3
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Hey bunuel! same answer same approach! I have been posting answers to some questions but m unaware of how to post formulas in the standard form. please give me a link so i can learn to do the same.
_________________
Spread some love..Like = +1 Kudos Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

ShashankDave wrote:
Hey bunuel! same answer same approach! I have been posting answers to some questions but m unaware of how to post formulas in the standard form. please give me a link so i can learn to do the same.

Check here: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

Hope it helps.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

dwalker0219 wrote:
Hey guys, I feel like the answer to my problem is something super obvious, but why is the area of the triangle 1/4 of the base (from subtracting the probability 3/4 from 1), resulting in an area of 3.
I got an area of 4, resulting from (Area of Circle)/(Area of Circle + Area of Triangle) = 3/4 (with Area of Circle = 12). I want to say if I was given a problem asking for the probability of red balls when there are 12 red balls and 4 blue balls, i would say the probability is 12/(12+4) = 3/4.

Thank you for the help........I'm slowly losing it with all these fractions, and positives and negatives, and less than greater than's, and that and it not having references, and primary purpase of passages.......

Check here: a-cylindrical-tank-has-a-base-with-a-circumference-of-105453.html#p1234048
_________________
Senior Manager  Joined: 08 Apr 2012
Posts: 346
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Bunuel wrote:
bhushan288 wrote:
hi guys...
can u help me out with this 1....
thnks in advance

A cylindrical tank has a base with a circumference of meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

Hi bhushan288, and welcome to Gmat Club.

Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.
Make sure you type the question in exactly as it was stated from the source.

Also:
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Original question is:

A cylindrical tank has a base with a circumference of $$4\sqrt{\pi{\sqrt{3}}$$ meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

A. $$\sqrt{2{\sqrt{6}}$$

B. $$\frac{\sqrt{6{\sqrt{6}}}}{2}$$

C. $$\sqrt{2{\sqrt{3}}$$

D. $$\sqrt{3}$$

E. $$2$$

Given: $$circumference=4\sqrt{\pi{\sqrt{3}}$$ and $$P(out)=\frac{3}{4}$$

Now, as the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4 then the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base and the triangle itself 1/4 of the are of the base.

Next: $$circumference=4\sqrt{\pi{\sqrt{3}}}=2\pi{r}$$ --> square both sides --> $$16\pi{\sqrt{3}}=4{\pi}^2{r}^2$$ --> $$4{\sqrt{3}}={\pi}{r}^2$$ --> $$area_{base}=\pi{r^2}=4{\sqrt{3}}$$;

The area of the equilateral triangle is 1/4 of the base: $$area_{equilateral}=\frac{1}{4}*4{\sqrt{3}}=\sqrt{3}$$ --> also the ares of the equilateral triangle is $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}$$, where $$a$$ is the length of a side --> $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3}$$ --> $$a=2$$.

Answer: E.

Hi Bunuel,

I missed the part where the triangle = 1/4 of the circle.
I did, however, get all the other results.
So what I did was (1-Area of triangle)/area of circle = 3/4
But I seem to get a different answer that you.
Have any idea why?
Senior Manager  Joined: 08 Apr 2012
Posts: 346
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

Bunuel wrote:
... also the ares of the equilateral triangle is $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}$$...

Answer: E.

Hi Bunuel,
The equation for the area of a triangle is only for an equilateral inscribed in a circle, is it not? is it for any triangle painted within a circle?
Math Expert V
Joined: 02 Sep 2009
Posts: 55275
Re: A cylindrical tank has a base with a circumference of  [#permalink]

### Show Tags

ronr34 wrote:
Bunuel wrote:
... also the ares of the equilateral triangle is $$area_{equilateral}=a^2*\frac{\sqrt{3}}{4}$$...

Answer: E.

Hi Bunuel,
The equation for the area of a triangle is only for an equilateral inscribed in a circle, is it not? is it for any triangle painted within a circle?

$$area_{equilateral}=side^2*\frac{\sqrt{3}}{4}$$ is for ANY EQUILATERAL triangle.

Check Triangles chapter of our Math Book: math-triangles-87197.html
_________________ Re: A cylindrical tank has a base with a circumference of   [#permalink] 27 Jul 2014, 15:27

Go to page    1   2    Next  [ 23 posts ]

Display posts from previous: Sort by

# A cylindrical tank has a base with a circumference of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  