M03-08

Question

Is triangle  ABC  equilateral?

(1)  AB = 1

(2)  BC + AC = 2

Bunuel · Accepted Answer

Official Solution:

The triangle is equilateral when all of its sides have the same length. 
 
Statement (1) by itself is insufficient. We don't know anything about the length of the other sides.
 
Statement (2) by itself is insufficient. Knowing that  BC + AC = 2 , doesn't give us enough information to be sure that the triangle is equilateral. Suppose  BC=1.1  and  AC=0.9 . 
 
Statements (1) and (2) combined are insufficient. Combining the two statements doesn't ensure that BC and AC equal exactly 1 each.

Answer: E

girishiyer · Answer

Hi,

I got C.

Since we know :  <C<A+B

We can easily say its not an equilateral triangle

pls brunei can you specify

Bunuel · Answer

How?

Case 1: all sides are of lengths 1.
Case 2: sides are: 0.9, 1, 1.1.

girishiyer · Answer

thanks bunuel for clarifying

TheNightKing · Answer

For first few seconds, I was thinking where is the image. lol Coming to the question, we can see that either the answer is C or E and that basically means one thing : Prove with one case that it is incorrect and you're good to go. Combined : AB=1 Assume BC and AC can only be nice sweet integers 1 and 1 the answer is Yes. It is an Eq Triangle. But if AB=1 BC=0.5 AC=1.5. well it is not possible because AB+BC is not greater than AC and that means it is not a triangle in the first place. But we can go further than that. AB=1 BC=0.8 AC=1.2. It is a triangle but not equilateral. We have enough information to declare E as the winner

WarriorWithin · Answer

A. AB = 1 - Other sides BC, AC can be / cannot be equal to AB --> Not Sufficient B. BC+AC=2 - Other side AB can be / cannot be equal to each BC and AC --> Not Sufficient C. We have AB = 1, BC+AC=2 Lets check if this values meets the criteria of properties of Triangles - 1. Any side of triangle will always be less than the sum of other two sides BC+AC>AB, AB+BC>AC, AC+AB>BC 2. Any side of triangle will always be greater than difference of the other two sides AC-BC No - It is not an equilateral triangle E is clearly the right answer.

M03-08

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