Solutions

Get detailed explanations to advanced GMAT questions.



Question

Is quadrilateral MNOP a square?

I. MN = NO = OP

II. Angle N and angle O are right angles.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Medium

Solution

Option C is the correct answer.


Option Analysis

Statement I is insufficient: tells us the lengths of three sides but this theory still could leave us with a fourth side that is longer/shorter than the rest, so insufficient.

Statement II is insufficient: Tells us that our quadrilateral is either a rectangle or a square, insufficient.

Together I and II, tell us that our quadrilateral is a square, because Statement II restricts the possible shapes that statement II can take, and combining the two tells us how long the fourth side in Statement I is, so sufficient.