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## Difficult Math Problem #88 - Geometry

tagged by: Roland2rule

This topic has 2 expert replies 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

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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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

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### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Fri Jan 12, 2018 6:35 am
800guy wrote:
[b]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
We can use the triangle inequality theorem, in which the sum of any two sides of a triangle must be greater than the third side. For Roman numeral I, since 5 + 7 = 12, which is not greater than 12, I cannot be true. For Roman numeral II since 2 + 4 = 6, which is not greater 10, II cannot be true, either.

However, in analyzing Roman numeral III, regardless of which two sides we select, the sum of any two lengths will always be greater than the third. Thus, III can be the lengths of the sides of a triangle.

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AMalik Junior | Next Rank: 30 Posts
Joined
15 Dec 2006
Posted:
15 messages
Fri Jan 19, 2007 10:19 am
800guy wrote:
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

maxim730 Senior | Next Rank: 100 Posts
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Fri Jan 19, 2007 10:50 am
Yeah, B

he length of the 2 smallest sides HAS to be greater than the 3rd side. So B.

800guy Master | Next Rank: 500 Posts
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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.

### Top Member

Roland2rule Legendary Member
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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.

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