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n is a positive integer

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by sanju09 » Wed May 02, 2012 3:04 am
The length of each of the sides of a triangle is a positive integer and n is a positive integer. If the length of one side is n + 10 and the length of another side is n + 12, then the shortest possible length of the third side is:
(A) n – 2
(B) n + 2
(C) n + 11
(D) 2
(E) 3



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by Anurag@Gurome » Wed May 02, 2012 11:26 pm
sanju09 wrote:The length of each of the sides of a triangle is a positive integer and n is a positive integer. If the length of one side is n + 10 and the length of another side is n + 12, then the shortest possible length of the third side is:
(A) n – 2
(B) n + 2
(C) n + 11
(D) 2
(E) 3



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The difference of any two sides in a triangle is always less than the third side.
Difference of two given sides = n + 12 - (n + 10) = 2, which implies that the minimum possible length of 3rd side = 3

The correct answer is E.
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