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

Question

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

Nikhil · Answer

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

GmatDaddy · Answer

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.

Answer: D

rahul16singh28 · Answer

Hi  amanvermagmat

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

amanvermagmat · Answer

Hello Rahul

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

rahul16singh28 · Answer

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.

amanvermagmat · Answer

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

rahul16singh28 · Answer

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 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.

rohialal · Answer

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

GmatDaddy · Answer

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 !

amanvermagmat · Answer

Hello Rumanshu

Yes I think you are correct. Question was alright in its original form also, thanks.

LevanKhukhunashvili · Answer

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

aserghe1 · Answer

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.

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

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