GMAT Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #5 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

True or false:  is scalene.

Statement 1: 

Statement 2: 

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question. 

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

By definition, a scalene triangle has three noncongruent sides.

Statement 1 alone states that two sides are noncongruent, but no information is given about whether or not third side  is congruent to either of the other sides.

Assume Statement 2 alone. In a triangle, sides opposite congruent angles are congruent, so it follows that . The triangle cannot be scalene.

Example Question #292 : Geometry

True or false:  is scalene.

Statement 1: 

Statement 2: 

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question. 

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question. 

Explanation:

By definition, a scalene triangle has three noncongruent sides. 

If , then  and , and the triangle is scalene.

If , then  and , but , so the triangle is not scalene.

The two statements together are insufficient.

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