BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Set of all values of d

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Set of all values of d

by gmattesttaker2 » Mon May 19, 2014 7:08 pm
Hello,

Can you please help with this:

Which of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?

A) 0<d<1
B) 0<d<5
C) 0<d<7
D) 1<d<5
E) 1<d<7

OA: E

Thanks,
Sri
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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 » Mon May 19, 2014 8:09 pm
gmattesttaker2 wrote: Which of the following inequalities indicates the set of all values of d for which the lengths of the three sides of a triangle can be 3,4, and d?

A) 0<d<1
B) 0<d<5
C) 0<d<7
D) 1<d<5
E) 1<d<7
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, 4 - 3 < d < 4 + 3
Simplify: 1 < d < 7
Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Mon May 19, 2014 8:40 pm
Hi Sri,

This question is actually written in such a way that if you know a bit about triangles, then you can logically eliminate all the wrong answers. Here's how.

The question does NOT state that the third side has to be an integer, so we have to keep an open mind about non-integers.

Notice how three of the answers are 0 < d. These 3 answers imply that the missing side could be "just above 0"; for practical purposes, the ONLY type of triangles that allow for that possibility are isosceles triangles - the two sides that we're given would have to be the SAME LENGTH for this option to exist. With sides of 3 and 4, we CANNOT have a side that's "just above 0." Eliminate A, B and C.

With the Pythagorean Theorem comes the "Magic Pythagorean Triples", one of which is the 3/4/5 right triangle. With sides of 3 and 4, the missing side COULD be a 5, so we need an answer that accounts for that possibility. Eliminate D.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1