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## OG 13 Problem

oquiella Master | Next Rank: 500 Posts
Joined
12 May 2015
Posted:
164 messages
3

#### OG 13 Problem

Tue Dec 22, 2015 3:08 pm
If K is an integer and 2
A. One
B. Two
C. Three
D. Four
E. Five

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9172 messages
Followed by:
472 members
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GMAT Score:
800
Thu Feb 15, 2018 7:05 pm
Hi All,

We're told that K is an integer and 2 < K < 7. We're asked for the number of different values of K that would create a triangle with sides of lengths 2, 7 and K.

This question is based on a math rule called the Triangle Inequality Theorem. In simple terms, it means that if you're dealing with a triangle, then the sum of ANY 2 sides will be greater than the 3rd side. For example, with a 3/4/5 right triangle....

3 + 4 > 5
3 + 5 > 4
4 + 5 > 3
So these 3 lengths (and these 3 inequalities) PROVE that we're dealing with an actual triangle.

In that same way, we can use the rule to determine when we're NOT dealing with an actual triangle... For example, you CANNOT have a triangle with sides of 1, 1 and 100 (because 1+1 is NOT greater than 100).

With this question, we're given two sides: 2 and 7 and we're asked to determine what the third side (K) could be. We're given a range of values for K and we're told that K must be an INTEGER. Since 2 + K must be GREATER than 7, the only possible value that fits all of the given information is K=6. Thus, there's only one value for K.

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

_________________
Contact Rich at Rich.C@empowergmat.com

Marty Murray Legendary Member
Joined
03 Feb 2014
Posted:
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GMAT Score:
800
Tue Dec 22, 2015 10:47 pm
Quote:
If K is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

A. One
B. Two
C. Three
D. Four
E. Five
For three line segments to work as a triangle, the lengths of any two of the segments have to add up to a sum greater than the length of the third. Otherwise two sides will not be long enough to connect with each other and with the ends of the third side.

The integers k such that 2 < k < 7 are 3, 4, 5 and 6.

See how many of those could form a triangle with sides 2, 7, and k.

If the lengths of the three segments were 2, 7 and 3, the segments 2 and 3 long would not be long enough to connect with each other and with the ends of the segment 7 long to form a triangle.

2 + 4 < 7 Doesn't work.

2 + 5 = 7 The only way to connect all the ends is to put them together flat. That's not a triangle.

2 + 6 > 7 -- 7 + 2 > 6 -- 7 + 6 > 2 That works.

So only K = 6 works and the correct answer is A.

_________________
Marty Murray
GMAT Coach
m.w.murray@hotmail.com
http://infinitemindprep.com/
In Person in the New York Area and Online Worldwide

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