Q: Is ABCD Square?
I. Angle B and Angle C are right angles.
II. AB=BC=CD
Please provide the explanation!
Is it a square?
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- aneesh.kg
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For a quadrilateral to be a square, all the four sides have to be equal and all the interior angles must be 90 degrees.
Statement (1): Can't be sure. The other two angles may both be 90 degrees or not.
INSUFFICIENT.
Statement (2): Can be any quadrilateral.
INSUFFICIENT.
Let's try to combine the two statements.
Draw a figure with AB=BC=CD and AB perpendicular to BC and BC perpendicular to CD.
You will notice that:
(i) AD is parallel to BC
(ii) AD = BC
That is, the fourth side has no choice but to be joined in a way so that ABCD forms a square.
[spoiler](C)[/spoiler] is the answer.
Let's modify the question a little bit?
modified Q1: (the modification is made bold)
Is ABCD Square?
I. Angle A and Angle C are right angles.
II. AB=BC=CD
modified Q2: (the modification is made bold)
Is ABCD Square?
I. Angle B and Angle C are right angles.
II. AB=CD
modified Q3: (the modification is made bold)
Is ABCD a Rectangle?
I. Angle B and Angle C are right angles.
II. AB=CD
Note: Keep making slight modifications to the problem and solving it. It's a great way to learn. You can seek the support of experts here in verifying your answers.
Statement (1): Can't be sure. The other two angles may both be 90 degrees or not.
INSUFFICIENT.
Statement (2): Can be any quadrilateral.
INSUFFICIENT.
Let's try to combine the two statements.
Draw a figure with AB=BC=CD and AB perpendicular to BC and BC perpendicular to CD.
You will notice that:
(i) AD is parallel to BC
(ii) AD = BC
That is, the fourth side has no choice but to be joined in a way so that ABCD forms a square.
[spoiler](C)[/spoiler] is the answer.
Let's modify the question a little bit?
modified Q1: (the modification is made bold)
Is ABCD Square?
I. Angle A and Angle C are right angles.
II. AB=BC=CD
modified Q2: (the modification is made bold)
Is ABCD Square?
I. Angle B and Angle C are right angles.
II. AB=CD
modified Q3: (the modification is made bold)
Is ABCD a Rectangle?
I. Angle B and Angle C are right angles.
II. AB=CD
Note: Keep making slight modifications to the problem and solving it. It's a great way to learn. You can seek the support of experts here in verifying your answers.
Aneesh Bangia
GMAT Math Coach
[email protected]
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GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
- tpr-becky
- GMAT Instructor
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Start with the definition of a square: four equal sides and four right angles.
statement 1 tells you that you have 2 right angles but does not tell you anything about the sides. insufficient.
STatement 2 tells you that you have 3 equal sides, but if one side is much smaller then this isn't a square - insufficient.
together - you have two right angles which means that you have three equal sides and at least 2 right angles, which will make for at least one set of parallel sides - with the third equal side it forces the fourth side to be equal and you have a square so the answer is C.
Best of Luck
statement 1 tells you that you have 2 right angles but does not tell you anything about the sides. insufficient.
STatement 2 tells you that you have 3 equal sides, but if one side is much smaller then this isn't a square - insufficient.
together - you have two right angles which means that you have three equal sides and at least 2 right angles, which will make for at least one set of parallel sides - with the third equal side it forces the fourth side to be equal and you have a square so the answer is C.
Best of Luck
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA