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 #51 : Triangles

True or false:  is scalene.

Statement 1: 

Statement 2: 

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question. 

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 sufficient to answer the question, but NEITHER 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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