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:

The circular base of an above ground swiming pool lies in a [#permalink]

Show Tags

02 Nov 2006, 09:49

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

77% (06:12) correct
23% (01:35) wrong based on 220 sessions

HideShow timer Statistics

Attachment:

pool.jpg [ 5.65 KiB | Viewed 3799 times ]

The circular base of an above ground swiming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure. point C is on the ground where the two sides of the fence meet. how far from the center of the pool's base is point A?

(1) The base has are 250 square feet. (2) The center of the base is 20 feet from point C

This problem sucks. What does "as shown in the figure" mean? Given that the distance from C to the center of the circle is 20 feet, I can tell you the radius of the circle to any arbitrary precision. So if you want it down to the nearest micron, I need only get measuring instruments up to the task. If this was physics class, I would say I have 1 (or 2) significant figure in statement 2 so I need only give you the radius to that many significant figures. I can do that with any number of measuring instruments.

You just need to find the radius of the circle. With the area, you can solve for R. Statement 2 adds nothing of value.

So what did you think of my post above? If I can tell you the radius to any precision you require, I can tell you the radius. Thus, statement 2 is sufficient (although I am sure that the person who wrote the problem wouldn't agree).

Re: The circular base of an above ground swiming pool lies in a [#permalink]

Show Tags

12 Jan 2013, 10:38

Hello!

Potentially a stupid question... When I reviewed the answer in the GMAT review book, I was wondering why statement 2 is wrong. If we know that the distance from C to Q (q being the center of the circle) is 20 can't we infer that triangle CQA is a right triangle that is 12-16-20 and therefore we know the other sides?

Potentially a stupid question... When I reviewed the answer in the GMAT review book, I was wondering why statement 2 is wrong. If we know that the distance from C to Q (q being the center of the circle) is 20 can't we infer that triangle CQA is a right triangle that is 12-16-20 and therefore we know the other sides?

Or is this logic flawed?

Thanks! Alex

Good question. Your assumption is correct but conclusion is not.

You are right, CQA IS a right triangle, because the tangent line (CA) is always at the 90 degree angle (perpendicular) to the radius (QA) of a circle.

So, we have that CQ=hypotenuse=20. BUT, knowing that hypotenuse equals to 20 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 12:16:20. Or in other words: if \(x^2+y^2=20^2\) DOES NOT mean that \(x=12\) and \(y=16\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=20^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=12\) and \(y=16\).

For example: \(x=1\) and \(y=\sqrt{399}\) or \(x=2\) and \(y=\sqrt{396}\)...

Re: The circular base of an above ground swiming pool lies in a [#permalink]

Show Tags

13 Jan 2013, 03:59

The distance between the center of base to point A - Radius of the circular pool.

A. Area = 250 square feet = 22/7 * r2..can find the radius. Sufficient B. Distance from center of pool to point C = 20 feet. Doesn't help to find the radius. Insufficient

Re: The circular base of an above ground swiming pool lies in a [#permalink]

Show Tags

25 May 2014, 14:33

Bunuel wrote:

alexpavlos wrote:

Hello!

Potentially a stupid question... When I reviewed the answer in the GMAT review book, I was wondering why statement 2 is wrong. If we know that the distance from C to Q (q being the center of the circle) is 20 can't we infer that triangle CQA is a right triangle that is 12-16-20 and therefore we know the other sides?

Or is this logic flawed?

Thanks! Alex

Good question. Your assumption is correct but conclusion is not.

You are right, CQA IS a right triangle, because the tangent line (CA) is always at the 90 degree angle (perpendicular) to the radius (QA) of a circle.

So, we have that CQ=hypotenuse=20. BUT, knowing that hypotenuse equals to 20 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 12:16:20. Or in other words: if \(x^2+y^2=20^2\) DOES NOT mean that \(x=12\) and \(y=16\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=20^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=12\) and \(y=16\).

For example: \(x=1\) and \(y=\sqrt{399}\) or \(x=2\) and \(y=\sqrt{396}\)...

Hope it's clear.

Hi Bunuel,

I ran into a similar issue but took it even further -- I inferred that triangle QAC is a 30.60.90. Not really sure my reasoning behind it come to think of it but that's what I ended up with. A 30.60.90 and a side, therefore statement 2 was sufficient.

Cant we assume that angle C is cut in half by the two triangles and therefore will be 30?

Potentially a stupid question... When I reviewed the answer in the GMAT review book, I was wondering why statement 2 is wrong. If we know that the distance from C to Q (q being the center of the circle) is 20 can't we infer that triangle CQA is a right triangle that is 12-16-20 and therefore we know the other sides?

Or is this logic flawed?

Thanks! Alex

Good question. Your assumption is correct but conclusion is not.

You are right, CQA IS a right triangle, because the tangent line (CA) is always at the 90 degree angle (perpendicular) to the radius (QA) of a circle.

So, we have that CQ=hypotenuse=20. BUT, knowing that hypotenuse equals to 20 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 12:16:20. Or in other words: if \(x^2+y^2=20^2\) DOES NOT mean that \(x=12\) and \(y=16\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=20^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=12\) and \(y=16\).

For example: \(x=1\) and \(y=\sqrt{399}\) or \(x=2\) and \(y=\sqrt{396}\)...

Hope it's clear.

Hi Bunuel,

I ran into a similar issue but took it even further -- I inferred that triangle QAC is a 30.60.90. Not really sure my reasoning behind it come to think of it but that's what I ended up with. A 30.60.90 and a side, therefore statement 2 was sufficient.

Cant we assume that angle C is cut in half by the two triangles and therefore will be 30?

Yes, angle C will be cut in half by CQ. But we don't know the measure of angle C. So, we cannot assume that it's 60 degrees and that half of it is 30 degrees.

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...