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:

bunuel any other wayout for this problem. i have drawn 3 triangles and done that way, is it ok. thanks

Yes, you can solve it with a triangle property which says that the length of any side of a triangle must be smaller than the sum of the other two sides.

Though you can naturally apply this property to any polygon and you won't need intermediary steps for solving.
_________________

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

08 Sep 2012, 02:29

3

This post received KUDOS

As mentioned by Bunuel, I will give another way to solve this problem using Triangle property.

Join P & R In triangle PQR, the known two sides are 3 & 2 units so third side (Let x) must be between 1<x<5 i.e. it can take any value 2,3 or 4 In other words the maximum & minimum values possible are 4 & 2 respectively

Join T & R In triangle PQR, the known two sides are 4 & 5 units so third side (Let y) must be between 1<x<9 i.e. it can take any value 2,3,4,5,6,7 or 8 In other words the maximum & minimum values possible are 8 & 2 respectively

We want to know the values possible for PT In triangle PRT, the range of two sides is 1<x<5 & 1<x<9 units so third side (PT) must be between (2-2)< PT <(8+4) or 0< PT<12 i.e. it can take any value 1,2,3,4,5,6,7....10,11 (assuming sides can take only integer values)

Thus both 5 & 10 are possible Thus Answer C

Hope it helps.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

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

Hi Bunuel,

The length of any side of a triangle must smaller than the sum of the other two sides. The same for pentagon: the length of any side of a pentagon must be smaller than the sum of the other four sides.

is this true only for triangle and pentagon or any other polygon? How can we determine it?
_________________

GMAT - Practice, Patience, Persistence Kudos if u like

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

18 Apr 2013, 06:50

2

This post received KUDOS

Bunuel wrote:

The length of any side of a triangle must smaller than the sum of the other two sides. The same for pentagon: the length of any side of a pentagon must be smaller than the sum of the other four sides.

Dear Bunuel, does this property apply to all quadrilaterals ? -- Thank you

The length of any side of a triangle must smaller than the sum of the other two sides. The same for pentagon: the length of any side of a pentagon must be smaller than the sum of the other four sides.

Dear Bunuel, does this property apply to all quadrilaterals ? -- Thank you

Yes, the length of any side of a polygon must be less than the sum of the lengths of the other sides.
_________________

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

17 May 2013, 06:32

2

This post received KUDOS

SrinathVangala wrote:

In Pentagon PQRST, PQ = 3,OR =5,RS =2 and ST =5.Which of the lengths 5,10 and 15 could be the value of PT?

Attachment:

The attachment Untitled.jpg is no longer available

A. 5 only B. 15 only C. 5 and 10 only D.10 and 15 only E. 5 , 10 and 15

Good one! The answer seems to be [C].

The easy way to approach this would be to consider the pentagon be comprised of 3 triangles as in the figure.

Let x and y be the diagonals under the quad which make the 3 triangles possible. Now by triangle property, we know x < QR + PQ = 8 ......(1) and y < RS + ST = 7 ...........(2)

Hence now in the interior triangle with sides x,y and PT, we further apply the triangle property: PT < x+y From above we already know by adding (1) and (2) x+y < 15, Hence we can say, that PT < 15. That rules out 15 off the options and 5, 10 can be possible values of the side!

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

17 May 2013, 06:36

Since there is no more information is given about the pentagon, only condition which has to be satisfied is that sum of any 4 sides must be larger than the fifth side. Now, 4 lengths are given as: 2,3,5,5. Fifth side must be smaller than sum of these 4, i.e must be smaller than 15, so 15 can't be the answer. About 5 and 10, there can not be any restriction, as the above rule is not broken in any of these cases. So, answer is c) 5 and 10 only.

In Pentagon PQRST, PQ = 3,OR =5,RS =2 and ST =5.Which of the lengths 5,10 and 15 could be the value of PT?

Attachment:

Untitled.jpg

A. 5 only B. 15 only C. 5 and 10 only D.10 and 15 only E. 5 , 10 and 15

Assuming OR is actually QR above, then this problem hinges on the fact that the fifth side of the pentagon must be shorter than the sum of the other four sides. If the four sides add up to 15 (3+5+2+5) then the fifth side cannot be 15, as this would form a line. Similarly, it cannot be greater than 15. It could, however, easily be 5 or 10, depending on the angles of the other arcs. Answer choice C.

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

16 Jan 2014, 02:33

1

This post received KUDOS

Bunuel wrote:

jainpiyushjain wrote:

Bunuel wrote:

The length of any side of a triangle must smaller than the sum of the other two sides. The same for pentagon: the length of any side of a pentagon must be smaller than the sum of the other four sides.

Dear Bunuel, does this property apply to all quadrilaterals ? -- Thank you

Yes, the length of any side of a polygon must be less than the sum of the lengths of the other sides.

Hi Bunnuel,

Is there a rule that pertains to the minimum length of polygons? I'm assuming that there is only one for triangles...

To piggy back on this question -- the links that you have provided state that the length of the 5th side has to be less than the sum of the other 4 sides. Is there anything governing the lower end? For example, in a triangle, the third side must be bigger than the difference of the two sides. Does a similar rule apply to pentagons and if they do, how do you compare which 2 sides?

My question just lies as to why we didn't prove/justify that 5 wasn't too small? In this case, we don't have an answer choice that just states that "10" is the value but if it did, are we to assume that 5 will automatically work?

Re: In pentagon PQRST, PQ=3, QR=2, RS=4,and ST=5. Which of the [#permalink]

Show Tags

30 May 2015, 02:44

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.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

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...