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A certain triangle has a perimeter of 24. Which of the following could

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A certain triangle has a perimeter of 24. Which of the following could [#permalink]

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New post 03 Sep 2017, 20:23
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Question Stats:

72% (00:41) correct 28% (00:30) wrong based on 32 sessions

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A certain triangle has a perimeter of 24. Which of the following could be the length of one of the sides?
I. 10
II. 12
III. 14
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III
[Reveal] Spoiler: OA

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Kudos [?]: 32 [1], given: 13

Manager
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Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73

Kudos [?]: 32 [0], given: 13

GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink]

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New post 03 Sep 2017, 20:26
Sum of any two sides of a triangle is greater than third side.
If one side is
I - 10, sum of other two is 14 possible
II- 12, sum of other two is 12 not possible (as sum of any two sides should be greater than third side)
III-14, sum of other two is 10 not possible (as sum of any two sides should be greater than third side)
Thus I only, option A
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Abhishek Parikh
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Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com

Kudos [?]: 32 [0], given: 13

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Re: A certain triangle has a perimeter of 24. Which of the following could [#permalink]

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New post 03 Sep 2017, 23:30
Given:
For a triangle a+b+c=24
Theory used: SUm of 2 sides of a triangle is always "greater" than 3rd side

1)a=10, so b+c=14
we can find different values of b and c to satisfy the condition.
Sufficient

2)a=12, so b+c=12,
Here sum of 2 sides becomes "equal to 3rd side". Not possible for a triangle.

3)a=14, so b+c=10,
Here sum of 2 sides becomes "less than 3rd side". Not possible for a triangle.

Answer: A

Kudos [?]: 108 [0], given: 66

Re: A certain triangle has a perimeter of 24. Which of the following could   [#permalink] 03 Sep 2017, 23:30
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A certain triangle has a perimeter of 24. Which of the following could

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