Last visit was: 14 Jul 2024, 07:38 It is currently 14 Jul 2024, 07:38
Toolkit
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

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.

If 3 and 8 are the lengths of two sides of a triangular region, which

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 08 Jul 2004
Posts: 322
Own Kudos [?]: 2203 [42]
Given Kudos: 0
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640710 [16]
Given Kudos: 85011
Director
Joined: 24 Sep 2005
Posts: 833
Own Kudos [?]: 1483 [7]
Given Kudos: 0
General Discussion
Senior Manager
Joined: 11 May 2004
Posts: 276
Own Kudos [?]: 154 [3]
Given Kudos: 0
Location: New York
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
1
Kudos
2
Bookmarks
the sum of the two sides must be greater than the third side. 3+8 =11
the difference of the two sides mut be less than the third side. 8-3=5

therefore the third side is between 5 and 11. Only B fulfills this.
Intern
Joined: 01 Aug 2011
Posts: 12
Own Kudos [?]: 14 [0]
Given Kudos: 15
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?
CEO
Joined: 26 Feb 2016
Posts: 2865
Own Kudos [?]: 5311 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
Bunuel wrote:
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

The only possibility for the third side of the triangle is 8
because the property of the triangle which is used over here is
the sum of any 2 sides must be larger than the third side.

Hence Option A(II only) is the answer choice
Current Student
Joined: 18 Aug 2016
Posts: 531
Own Kudos [?]: 585 [0]
Given Kudos: 198
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
Bunuel wrote:
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Only possible value is 8 as 5<third side<11

A
Senior SC Moderator
Joined: 22 May 2016
Posts: 5327
Own Kudos [?]: 35754 [0]
Given Kudos: 9464
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
Bunuel wrote:
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

The third side of a triangle is always shorter than the sum of the other two sides:

x < 3 + 8
x < 11

AND the third side must be greater than the difference between the other two sides

x > 8 - 3
x > 5
5 < x

Together:

5 < x < 11

Third side x cannot be 5 or 11.

Only Option II satisfies the triangle inequality theorem.

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
1
Bookmarks
Hi All,

We're told that 3 and 8 are the lengths of two sides of a triangular region. We're asked which of the following values (3, 8 and 11) could be the length of the third side. This question is based on the Triangle Inequality Theorem and requires just a little Arithmetic to solve.

To start, when you have two sides of a triangle, the SMALLEST the third side could be would be just a little bit MORE than the DIFFERENCE of the two sides you have. Here, that's 8 - 3 = 5. If the third side was EXACTLY 5, then you would NOT have a triangle - you'd have a line of 8 on top of another line of 8. By making that third side just a little bigger than 5, you would then have a triangle.

In that same way, the LARGEST the third side could be would be just a little bit LESS than the SUM of the two sides. Here, that's 3 + 8 = 11. If the third side was EXACTLY 11, then you would NOT have a triangle - you'd have a line of 11 on top of another line of 11. By making that third side just a little less than 11, you would then have a triangle.

Thus, that third side falls into the following range: 3 < third side < 11. Based on the three given options, only a side of 8 is possible.

GMAT assassins aren't born, they're made,
Rich
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30796 [1]
Given Kudos: 799
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
1
Kudos
Top Contributor
saurya_s wrote:
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 8
III. 11

(A) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

So, for this question: 8 - 3 < third side < 8 + 3
Simplify: 5 < third side < 11

So, the third side must be LONGER than 5 and SHORTER than 11

Cheers,
Brent
Non-Human User
Joined: 09 Sep 2013
Posts: 33968
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
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: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
Moderator:
Math Expert
94342 posts