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## Difficult Math Problem #88 - Geometry

tagged by: Roland2rule

This topic has 1 expert reply and 4 member replies
800guy Master | Next Rank: 500 Posts
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#### Difficult Math Problem #88 - Geometry

Fri Jan 19, 2007 9:32 am
Which of the sets of numbers can be used as the lengths of the sides of a triangle?

I. [5,7,12]
II. [2,4,10]
III. [5,7,9]

A. I only
B. III only
C. I and II only
D. I and III only
E. II and III only

from 'difficult math problems' problem set. OA coming after some people attempt answers/explanations

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### Top Member

Roland2rule Master | Next Rank: 500 Posts
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Sun Dec 03, 2017 8:26 am
The longest side of a triangle must be less than the sum of the two other sides.
Option I {5, 7, 12}
The longest side is 12
and 12 = 5+7
Since, 12 is not less than 5+7 thus thisoption is invalid.

Option II : {2, 4, 10}
The longest side is 10 which is greater than 2+4=6.Thus, this option is invalid.

Option III : {5, 7, 9}
The longest side is 9, which is less than 5+7=12. Since this agrees with the rule stated above, this option is valid.
Only III is correct.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8954 messages
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GMAT Score:
800
Sun Dec 03, 2017 7:24 pm
Hi All,

Roland2rule's approach to this question is spot-on, so I won't rehash any of that math here. It's worth noting that Roman Numeral questions are often designed so that you don't necessarily have to work through all 3 Roman Numerals... IF you're paying attention to how the answer choices are written. Here, once you've proven that Roman Numeral 1 and Roman Numeral 2 are not possibilities, you can select the correct answer (and you don't even have to work on Roman Numeral 3).

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Top Member

Roland2rule Master | Next Rank: 500 Posts
Joined
30 Aug 2017
Posted:
405 messages
Followed by:
2 members
Sun Dec 03, 2017 8:26 am
The longest side of a triangle must be less than the sum of the two other sides.
Option I {5, 7, 12}
The longest side is 12
and 12 = 5+7
Since, 12 is not less than 5+7 thus thisoption is invalid.

Option II : {2, 4, 10}
The longest side is 10 which is greater than 2+4=6.Thus, this option is invalid.

Option III : {5, 7, 9}
The longest side is 9, which is less than 5+7=12. Since this agrees with the rule stated above, this option is valid.
Only III is correct.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8954 messages
Followed by:
468 members
2867
GMAT Score:
800
Sun Dec 03, 2017 7:24 pm
Hi All,

Roland2rule's approach to this question is spot-on, so I won't rehash any of that math here. It's worth noting that Roman Numeral questions are often designed so that you don't necessarily have to work through all 3 Roman Numerals... IF you're paying attention to how the answer choices are written. Here, once you've proven that Roman Numeral 1 and Roman Numeral 2 are not possibilities, you can select the correct answer (and you don't even have to work on Roman Numeral 3).

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11
Mon Jan 22, 2007 4:57 pm
OA:

For any side of a triangle. Its length must be greater than the difference between the other two sides, but less than the sum of the other two sides.

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