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:

I is a recycled 30:60:90 triangle---> so no obtuse triangle while for II & III it is possible to construct a triangle with atleast one obtuse angle

Dear mansoorfarooqui, You answered the question correctly, but with all due respect, a 6-9-10 triangle has absolutely nothing to do with a 30-60-90 triangle. The sides of the latter involve irrational number ratios, no matter what numbers are chosen for the lengths. The 6-9-10 triangle is an triangle with three acute angles. Mike
_________________

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

02 Jan 2013, 12:00

hi mikemcgarry,

thanks for the clarification.. 6-9-10 is not a recycled triangle.. 6-8-10 would have been one in which one angle would be 90 and other two have to be acute... so my mistake..

Here's an even more challenging problem along the same lines.

Attachment:

triangle in circle.JPG [ 19.46 KiB | Viewed 2552 times ]

In the diagram above, AB = 10 is the diameter of the circle, and AC = 6. Given that point C is inside the circle, which could be the length of BC? I. 7 II. 8 III. 9

(A) I (B) II (C) III (D) I & II (E) II & III

The information at the blog link above will help to solve this question. I will post an OA if folks are curious.

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

26 Mar 2013, 15:28

1

This post received KUDOS

2

This post was BOOKMARKED

My method to determine such problems is by using the pythogoras theorem.

If (largest side)^2 > Sum of square of other 2 sides then the triangle is OBTUSE TRIANGLE If (largest side)^2 = Sum of square of other 2 sides then the triangle is RIGHT ANGLE TRAINGLE If (largest side)^2 < Sum of square of other 2 sides then the triangle is ACUTE TRIANGLE

Tr1 has sides 6-9-10: 100 < 81+36 hence acute Tr. Tr2 has sides 8-14-17: 289 > 196+64 = 260 hence OBTUSE Tr Tr 3 has sides 5-12-14: 196 > 25+144 = 169 hence again OBTUSE Tr.

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

27 Mar 2013, 20:40

[quote="mikemcgarry"]Consider the following three triangles

I. a triangle with sides 6-9-10 II. a triangle with sides 8-14-17 III. a triangle with sides 5-12-14

Which of the following gives a complete set of the triangles that have at least one obtuse angle, that is, an angle greater than 90°?

(A) I (B) II (C) III (D) I & II (E) II & III

Basically, there is just one formula for questions like these. For any triangle,\(c^2 = a^2 + b^2 - 2abCos(C)\), where a,b,c and angles A,B,C follow the normal convention. Now, for an acute triangle, the value of 0<Cos(C)<1 --> \(a^2+b^2>c^2\). For obtuse angles, -1<Cos(C)<0 -->\(c^2>a^2+b^2\) and for C = 90 degrees, we have Pythagoras theorem. Trigonometry, is not tested on GMAT(Quoting Bunuel on this), yet doesn't hurt to know some thing useful.
_________________

Basically, there is just one formula for questions like these. For any triangle,\(c^2 = a^2 + b^2 - 2abCos(C)\), where a,b,c and angles A,B,C follow the normal convention. Now, for an acute triangle, the value of 0<Cos(C)<1 --> \(a^2+b^2>c^2\). For obtuse angles, -1<Cos(C)<0 -->\(c^2>a^2+b^2\) and for C = 90 degrees, we have Pythagoras theorem. Trigonometry, is not tested on GMAT(Quoting Bunuel on this), yet doesn't hurt to know some thing useful.

Dear vinaymimani, you obviously have a strong background in math and have studied trigonometry already, so for you, thinking about these questions using the Law of Cosines is perfectly fine. I would caution you, though --- some people studying for the GMAT haven't done any math at all since high school Algebra II ---- these folks are struggling just to remember basic algebra & geometry, have never even met Cosine, and have no earthly clue even what trigonometry is. I guess I would caution you against cavalierly saying, "[it] doesn't hurt to know some thing useful" ----- if folks who are struggling to remember even how to solve for x or what properties a triangle has also are led to believe that there's something about the Law of Cosines they need to understand, that very much could hurt both their studying and their fragile mathematical self-confidence. Always remember --- there's a very wide audience for anything you post on this site. With great respect, Mike
_________________

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

28 Mar 2013, 09:29

mikemcgarry wrote:

Here's an even more challenging problem along the same lines.

Attachment:

triangle in circle.JPG

In the diagram above, AB = 10 is the diameter of the circle, and AC = 6. Given that point C is inside the circle, which could be the length of BC? I. 7 II. 8 III. 9

(A) I (B) II (C) III (D) I & II (E) II & III

The information at the blog link above will help to solve this question. I will post an OA if folks are curious.

Mike

Answer (A).

The Line BC would have maximum length when the opposite angle CAB would be as big as possible. In order to increase this angle the point C could touch the circle at some point. At that point we will have Right angle triangle with right angle at ACB.

BC = sqrt (100 - 36) BC = 8 So BC can be less than 8 only 7 satisfies.

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

28 Mar 2013, 09:30

1

This post received KUDOS

mikemcgarry wrote:

vinaymimani wrote:

Basically, there is just one formula for questions like these. For any triangle,\(c^2 = a^2 + b^2 - 2abCos(C)\), where a,b,c and angles A,B,C follow the normal convention. Now, for an acute triangle, the value of 0<Cos(C)<1 --> \(a^2+b^2>c^2\). For obtuse angles, -1<Cos(C)<0 -->\(c^2>a^2+b^2\) and for C = 90 degrees, we have Pythagoras theorem. Trigonometry, is not tested on GMAT(Quoting Bunuel on this), yet doesn't hurt to know some thing useful.

Dear vinaymimani, you obviously have a strong background in math and have studied trigonometry already, so for you, thinking about these questions using the Law of Cosines is perfectly fine. I would caution you, though --- some people studying for the GMAT haven't done any math at all since high school Algebra II ---- these folks are struggling just to remember basic algebra & geometry, have never even met Cosine, and have no earthly clue even what trigonometry is. I guess I would caution you against cavalierly saying, "[it] doesn't hurt to know some thing useful" ----- if folks who are struggling to remember even how to solve for x or what properties a triangle has also are led to believe that there's something about the Law of Cosines they need to understand, that very much could hurt both their studying and their fragile mathematical self-confidence. Always remember --- there's a very wide audience for anything you post on this site. With great respect, Mike

You seem to have missed the entire point of my post. I had written "Trigonometry is NOT tested on GMAT". That actually means my post was just an additional way of solving. And as for the wide audience reading this post, I personaly feel there is nothing wrong in sharing something new, as long as it is not WRONG. There is nothing cavalier about this post. Just a matter of choice for the thousands who are on this site.

Hi Mike could you please provide the official answer and explanation to the problem with the circle. Thanks, Raj

Dear Raj

As I discuss in this post: http://magoosh.com/gmat/2012/re-thinkin ... le-obtuse/ we can use the Pythagorean Theorem to determine, from the three sides of a triangle, whether the triangle is right, acute, or obtuse. I'll ask you to look at that page for the detailed discussion, but the nutshell summary is: If a^2+ b^2 = c^2, then the triangle is a right triangle. If a^2+ b^2 > c^2, then the triangle is a acute triangle. If a^2+ b^2 < c^2, then the triangle is a obtuse triangle. In all of these, of course, I am assuming a < b < c.

We have to combine this with another geometry idea ----- if the vertex an angle is on a circle, and the rays of angle pass through the two endpoints of a diameter of the circle, then the angle is a right angle. See this blog: http://magoosh.com/gmat/2012/inscribed- ... -the-gmat/

If BC = 8, then 6^2 + 8^2 = 10^2, and it's a right angle, which would mean point C would be on the circle, instead of inside the circle. If we made BC bigger than 8, that would push C further away, outside of the circle. Making BC smaller than 8 pulls it into the circle, so 7 is the only possible length for BC, and the OA for this question is (A).

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

10 Apr 2015, 05:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Which of the following gives a complete set of the triangles [#permalink]

Show Tags

07 Sep 2016, 01:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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...