length of the third side

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EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

length of the third side

by EricKryk » Fri Jan 24, 2014 9:27 am

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

Quote

Source: Beat The GMAT — Problem Solving | Fri Jan 24, 2014 9:27 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 24, 2014 9:31 am

EricKryk 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

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
Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 am; Thanked: 335 times; Followed by:98 members

by Patrick_GMATFix » Fri Jan 24, 2014 9:41 am

the length of the 3rd side of any triangle is greater than the positive difference between the other two side lengths, but less than the sum of the other two side lengths. The solution below is taken from the GMATFix App.