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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

28 Nov 2010, 01:04

5

This post received KUDOS

22

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

56% (02:07) correct 44% (01:46) wrong based on 581 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?

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?

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.

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 --> \(area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3}\) --> \(a=2\).

Re: Probability Triangle(700 lvl Qn ) [#permalink]

Show Tags

16 Mar 2011, 06:13

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.

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

Re: Probability Triangle(700 lvl Qn ) [#permalink]

Show Tags

16 Mar 2011, 06:32

1

This post received KUDOS

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.
_________________

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.
_________________

Re: A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

11 Jun 2013, 06:29

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

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

Re: A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

15 Nov 2013, 20:43

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.......

Re: A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

16 Nov 2013, 02:02

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.
_________________

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.

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.......

Re: A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

26 Jun 2014, 13:57

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?

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.

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?

Re: A cylindrical tank has a base with a circumference of [#permalink]

Show Tags

27 Jul 2014, 06:11

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?

... 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.