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If 4 and 11 are the lengths of two sides of a triangular region, which

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Bunuel
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If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   27 Jul 2016, 01:44
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If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 13
III. 15

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
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B
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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   27 Jul 2016, 02:36
Bunuel wrote:
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 13
III. 15

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III



Relationship of the Sides of a Triangle :
The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

i.e let us assume the third side be c and other sides be a and b, then as per rule

c > a - b and c < a + b.

Let's take options

option 1. the three sides will be 5 , 4 and 11..

then 11 > 5-4 --Yes
11 < 4+9...NO

option 2... 13, 4 and 11.

then 13 > 11-4...Yes
13 < 11+4...Yes

Option 3..15 ,4 and 11.

15 < 11+4...No
15 > 11-4...Yes...

Only 13 is correct .

IMO option B is correct..

OA please...will correct if I missed anything.
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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   27 Jul 2016, 07:56
Bunuel wrote:
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 13
III. 15

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III


The sum of the lengths of any two sides of a triangle must be greater than the third side.

I.
\(4 + 11 > 5\\\\
4 + 5 > 11 {\color{red}{\text{ false}}}\\\\
11 + 5 > 4\)

II.
\(4 + 11 > 13\\\\
4 + 13 > 11\\\\
11 + 13 > 4\)

III.
\(4 + 11 > 15 {\color{red}{\text{ false}}}\\\\
4 + 15 > 11\\\\
11 + 15 > 4\)

Show Spoiler
B. II only
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Divyadisha
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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   27 Jul 2016, 09:57
Bunuel wrote:
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 13
III. 15

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III


Length of third side< sum of other two sides and >difference of two sides

4+11>L>11-4
15>L>7

Only B fits in the condition
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LogicGuru1
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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   30 Jul 2016, 07:42
Bunuel wrote:
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5
II. 13
III. 15

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III


A + B > C

First case:- when one side is 5, others are 4 and 11
4+5>11 Nope
No need to work anymore on this case

Second case :- when one side is 13, others are 4 and 11
4+11>13 Yes
4+13>11 Yes
11+13>4 Yes

Third case :- when one side is 15, others are 4 and 11
4+11>15 Nope
No need to work anymore on this case

ANSWER B
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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   10 May 2019, 04:48
Third side should fallen between as follows.

11-3 < thirdside < 11+3

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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink] New post   02 Dec 2020, 13:32
Hello from the GMAT Club BumpBot!

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Re: If 4 and 11 are the lengths of two sides of a triangular region, which [#permalink]
02 Dec 2020, 13:32
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