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
MediumSolution
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.