A triangle (non-degenerate) has two sides of lengths 5 and 2. What val

Question

A triangle (non-degenerate) has two sides of lengths 5 and 2. What value could the length of the third side be if it is an odd integer number?

A. 3
B. 1
C. 5
D. 9
E. 7

Showmeyaa · Answer

As per the triangle inequality theorem:
The third side has to be more than the difference and less than the sum of the other 2 sides.
Algebraically:
5 - 2 < third side < 5 + 2
3 < third < 7
Possible values of third side are 4, 5, 6
Since, the third side is an odd number. Only 5 holds true!
IMO, (C)!

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=64755

Bumping for discussion. Try this one and get Kudos for a correct solution!!!!

jdcsantos · Answer

Triangles properties:
the sum of any 2 sides > any single side
The difference of any 2 sides < any single side

Now we have two sides a=5, b=2
a+b =7 must be greater than the third side
a-b = 3 must be smaller than the third side
Let's say x is the third side:
3<x<7 
Since there is a restriction (x is an ODD integer)
 5 is the only choice

Correct answer C

A triangle (non-degenerate) has two sides of lengths 5 and 2. What val

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A triangle (non-degenerate) has two sides of lengths 5 and 2. What val

Prep Toolkit

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