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# Is it possible to form a triangle with its three sides as 'a', 'b' and

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DS Forum Moderator
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Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 20:46
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Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively, such that a, b and c are all positive numbers?

(1) a + b < c

(2) a - b < c
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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Updated on: 21 Jul 2018, 20:58
To find whether a triangle can be formed with its three sides as 'a', 'b' and 'c' units respectively

Statement 1

a + b < c

Using the sides property of triangle we know that the sum of any two sides of triangle must be greater than the third side

Hence we cannot form a triangle with sides a, b and c and satisfying a + b < c

Statement 1 is sufficient to say we cannot form such a triangle

Statement 2

a - b < c

Again, using the sides property of triangle we know that the difference of any two sides of triangle must be less than the third side

=> We can form a triangle with the lengths a, b and c

Hence we can form a triangle with sides a, b and c and satisfying a - b < c

Statement 2 is sufficient to say we can form such a triangle

Hence option D
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Originally posted by workout on 21 Jul 2018, 20:57.
Last edited by workout on 21 Jul 2018, 20:58, edited 1 time in total.
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 20:57
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively?

(1) a + b < c

(2) a - b < c

For a Triangle with sides a, b and c, the following two properties hold. ALWAYS:
1. Sum of any two sides of a triangle is always greater than the third side.
2. Difference of any two sides is always lesser than the third side.

Now, coming back to question.

Statement 1: a + b < c
This implies that the sum of two sides is less than the third side.
Hence it is not possible to form a triangle.

Statement 1: a - b < c
This implies that the difference of two sides is lesser than the third side.
Hence such a triangle is possible.

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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:04
1
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively?

(1) a + b < c

(2) a - b < c

Hi amanvermagmat

In the question, its not mentioned that a,b,c >0 or not. Hence, E. Not sure if I am missing anything.
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:07
rahul16singh28 wrote:
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively?

(1) a + b < c

(2) a - b < c

Hi amanvermagmat

In the question, its not mentioned that a,b,c >0 or not. Hence, E. Not sure if I am missing anything.

Hello Rahul

Thanks for pointing that out. I have now edited the question to mention that a, b, c are all positive numbers.
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:21
amanvermagmat wrote:
rahul16singh28 wrote:
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively?

(1) a + b < c

(2) a - b < c

Hi amanvermagmat

In the question, its not mentioned that a,b,c >0 or not. Hence, E. Not sure if I am missing anything.

Hello Rahul

Thanks for pointing that out. I have now edited the question to mention that a, b, c are all positive numbers.

Thanks amanvermagmat

As a,b,c > 0, by combining the two (i.e. by subtracting the two equations) we get b < 0. But as per question b > 0. I see a contradiction here, can you help me to point out the flaw or the way forward. As I understand, the statements shouldn't contradict the question statement.
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:30
1
As a,b,c > 0, by combining the two (i.e. by subtracting the two equations) we get b < 0. But as per question b > 0. I see a contradiction here, can you help me to point out the flaw or the way forward. As I understand, the statements shouldn't contradict the question statement.[/quote]

Hello

As per my understanding, we cannot subtract inequalities which are in the same direction. We can only add them.
So on adding the two inequations, we get a+b+a-b < c+c OR 2a < 2c OR a < c
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:51
amanvermagmat wrote:
As a,b,c > 0, by combining the two (i.e. by subtracting the two equations) we get b < 0. But as per question b > 0. I see a contradiction here, can you help me to point out the flaw or the way forward. As I understand, the statements shouldn't contradict the question statement.

Hello

As per my understanding, we cannot subtract inequalities which are in the same direction. We can only add them.
So on adding the two inequations, we get a+b+a-b < c+c OR 2a < 2c OR a < c[/quote]

Thanks amanvermagmat. The answer should be A.

Statement I: As per property of triangle, sum of two sides must be greater than third side. So, not possible.

Statement II: Let $$(a,b,c) = (0.5,1,0.5)$$ --> The Traingle cannot be formed as it violates property of Triangle.
Let $$(a,b,c) = (2,1,4)$$ --> The traingle can be formed as its in accordance with Property of Triangle.

Hence, A.
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 22:55
IMO A.

Statement 1: It is clear . C>a+b. Not possible to form a triangle. Hence a clear no
Statement 2: c+b>a. but what about other combinations. a+b / a+c. Hence not clear.

Please clarify if I am wrong
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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21 Jul 2018, 23:18
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively, such that a, b and c are all positive numbers?

(1) a + b < c

(2) a - b < c

amanvermagmat I think it was clear in the previous version also. The question stated " triangle with its three sides as 'a', 'b' and 'c' units".
Length of the sides can never be of non-positive unit length !
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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22 Jul 2018, 09:46
Rumanshu1990 wrote:
amanvermagmat wrote:
Is it possible to form a triangle with its three sides as 'a', 'b' and 'c' units respectively, such that a, b and c are all positive numbers?

(1) a + b < c

(2) a - b < c

amanvermagmat I think it was clear in the previous version also. The question stated " triangle with its three sides as 'a', 'b' and 'c' units".
Length of the sides can never be of non-positive unit length !

Hello Rumanshu

Yes I think you are correct. Question was alright in its original form also, thanks.
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Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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22 Jul 2018, 10:08
First thing to mention:
In DS the statements don't contradict each other, If you arrive that such triangle doesn't exist with first statement and such triangle exists with second statement, the first thing you should do is to check the statements once again and detect the trap

1st statement: I dont see any problem, there is a rule and according to this rule such Triangle cannot exist-- Suffic
2nd statement: Here we have a trap, the rule says: The Positive difference of any two sides of triangle must be less than the third side. we dont know a-b is a positive difference or not. a=5 b=7 c=8 Such triangle has a right to exist but a-b<c as a-b is a negative number and always will be less than positive third side. -- Insuff.

IMO
Ans: A
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Re: Is it possible to form a triangle with its three sides as 'a', 'b' and  [#permalink]

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27 Jul 2018, 15:43
I dont understand why Statement 2 alone is not sufficient.

We're given a-b<c, which can be re-arranged as a<b+c. This means that the sum of 2 sides is greater than the 3rd side, which is always true for a triangle. Thus, it's possible to form a triangle with sides a,b,c.
Re: Is it possible to form a triangle with its three sides as 'a', 'b' and &nbs [#permalink] 27 Jul 2018, 15:43
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