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# Is a+b>c? 1) a, b, and c represent three different lengths of the s

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Senior SC Moderator
Joined: 14 Nov 2016
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Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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23 Feb 2017, 19:07
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Is $$a+b>c$$?

1) a, b, and c represent three different lengths of the sides of a certain triangle

2) $$a^2+b^2=c^2$$

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Director
Joined: 05 Mar 2015
Posts: 980
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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24 Feb 2017, 08:07
AustinKL wrote:
Is $$a+b>c$$?

1) a, b, and c represent three different lengths of the sides of a certain triangle

2) $$a^2+b^2=c^2$$

(1) sum of any two sides of triangle is always> third side......suff

(2) if a= 3 , b= 4 and c= 5 ...Yes
if a= 3 , b= -4 and c= 5 ...No
insuff

Ans A
Senior SC Moderator
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Posts: 1322
Location: Malaysia
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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04 May 2017, 19:08
ziyuen wrote:
Is $$a+b>c$$?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) $$a^2+b^2=c^2$$

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, $$a-b<c<a+b$$ appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

Bunuel & MathRevolution Could the side of a triangle be negative value?
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Director
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Posts: 980
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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04 May 2017, 19:24
ziyuen wrote:
ziyuen wrote:
Is $$a+b>c$$?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) $$a^2+b^2=c^2$$

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, $$a-b<c<a+b$$ appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

Bunuel & MathRevolution Could the side of a triangle be negative value?

ziyuen

but for the instance, please let me know from where u r assuming the option 2 relates to any triangle??
a,b,c are independent values and they are not meant for any triangle

hope it helps
Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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04 May 2017, 19:55
rohit8865 wrote:
ziyuen wrote:
ziyuen wrote:
Is $$a+b>c$$?

(1) a, b, and c represent three different lengths of the sides of a certain triangle

(2) $$a^2+b^2=c^2$$

OFFICIAL EXPLANATION

According to the characteristics of a certain triangle, if you let a, b, and c represent the 3 different side lengths of a triangle, $$a-b<c<a+b$$ appears often.

In other words, the sum of the lengths of the two sides is longer than the length of the other side.

(1) The condition is always yes. Sufficient.

(2) It is not about the Pythagorean Theorem of a right triangle. If (a,b,c)=(3,4,5), it is yes, but if (-3,-4,5), it is no. Insufficient.

Bunuel & MathRevolution Could the side of a triangle be negative value?

ziyuen

but for the instance, please let me know from where u r assuming the option 2 relates to any triangle??
a,b,c are independent values and they are not meant for any triangle

hope it helps

rohit8865

https://gmatclub.com/forum/math-triangles-87197.html

• A Pythagorean triple consists of three positive integers $$a$$, $$b$$, and $$c$$, such that $$a^2 + b^2 = c^2$$. Such a triple is commonly written $$(a, b, c)$$, and a well-known example is $$(3, 4, 5)$$. If $$(a, b, c)$$ is a Pythagorean triple, then so is $$(ka, kb, kc)$$ for any positive integer $$k$$. There are 16 primitive Pythagorean triples with c ≤ 100:
(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97).
_________________

"Be challenged at EVERY MOMENT."

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"Each stage of the journey is crucial to attaining new heights of knowledge."

Manager
Joined: 16 Jan 2017
Posts: 65
GMAT 1: 620 Q46 V29
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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05 May 2017, 14:41
I am confused as to the explanation given by some members. how can the side of a triangle be negative??
Intern
Joined: 25 Apr 2016
Posts: 25
Concentration: Entrepreneurship, Marketing
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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11 May 2017, 18:58
rohit8865 wrote:
AustinKL wrote:
Is $$a+b>c$$?

1) a, b, and c represent three different lengths of the sides of a certain triangle

2) $$a^2+b^2=c^2$$

(1) sum of any two sides of triangle is always> third side......suff

(2) if a= 3 , b= 4 and c= 5 ...Yes
if a= 3 , b= -4 and c= 5 ...No
insuff

Ans A

How can the side of a triangle be negative?
Manager
Joined: 27 Jun 2015
Posts: 66
WE: Information Technology (Computer Software)
Re: Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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05 Oct 2017, 19:44
ishitam wrote:
rohit8865 wrote:
AustinKL wrote:
Is $$a+b>c$$?

1) a, b, and c represent three different lengths of the sides of a certain triangle

2) $$a^2+b^2=c^2$$

(1) sum of any two sides of triangle is always> third side......suff

(2) if a= 3 , b= 4 and c= 5 ...Yes
if a= 3 , b= -4 and c= 5 ...No
insuff

Ans A

How can the side of a triangle be negative?

ishitam ,
Please consider the 2nd statement, independently, as just another algebraic equation. Yes it does represent Pythagoras theorem, but there is no where mentioned that a, b,c are sides of triangle in question stem.
2nd is a classic trap statement, wherein we do not completely remove the context given in statement 1 and assume something which is not present in statement 2.
Senior Manager
Joined: 02 Apr 2014
Posts: 486
GMAT 1: 700 Q50 V34
Is a+b>c? 1) a, b, and c represent three different lengths of the s  [#permalink]

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30 Nov 2017, 14:34
a+b > c?

Statement 1:
Property of a triangle, sum of any two sides is greater than the third side, hence a + b > c, sufficient

Statement 2:
if a, b, c -> pythogorian triplet, say {a = 3, b = 4, c = 5}, then a + b > c,
if a = 0, b = 0, c = 0, then $$a^2 + b^2 = c^2$$, but a +b = c, not sufficient

Is a+b>c? 1) a, b, and c represent three different lengths of the s &nbs [#permalink] 30 Nov 2017, 14:34
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