Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(1) AC is perpendicular to BD. The diagonals are perpendicular to each other: ABCD could be a kite (answer NO), a rhombus (answer YES) or a square, which is just a special type of rhombus (answer YES). Not sufficient.

(2) AB+CD=BC+DA. The sum of opposite sides are equal. Clearly insufficient.

(1)+(2) ABCD could be a kite (see the diagram below) - answer NO or a square/rhombus - answer YES. Not sufficient.

Re: If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

03 Nov 2015, 05:04

Bunuel wrote:

tt11234 wrote:

If ABCD is a quadrilateral, is AB=BC=CD=DA ?

1.AC is perpendicular to BD 2.AB+CD=BC+DA

please explain!! thanks~

If ABCD is a quadrilateral, is AB=BC=CD=DA ?

(1) AC is perpendicular to BD. The diagonals are perpendicular to each other: ABCD could be a kite (answer NO), a rhombus (answer YES) or a square, which is just a special type of rhombus (answer YES). Not sufficient.

(2) AB+CD=BC+DA. The sum of opposite sides are equal. Clearly insufficient.

(1)+(2) ABCD could be a kite (see the diagram below) - answer NO or a square/rhombus - answer YES. Not sufficient.

Answer: E.

Hi Bunuel,

Could you please help me understand why can't ABCD be a kite? Thanks.

(1) AC is perpendicular to BD. The diagonals are perpendicular to each other: ABCD could be a kite (answer NO), a rhombus (answer YES) or a square, which is just a special type of rhombus (answer YES). Not sufficient.

(2) AB+CD=BC+DA. The sum of opposite sides are equal. Clearly insufficient.

(1)+(2) ABCD could be a kite (see the diagram below) - answer NO or a square/rhombus - answer YES. Not sufficient.

Answer: E.

Hi Bunuel,

Could you please help me understand why can't ABCD be a kite? Thanks.

The solution says that ABCD can be a kite.
_________________

If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

03 Nov 2015, 08:16

damn, please mention that the diagonals are perpendicular. I was thinking, how the hell can 2 different sides be perpendicular to each other? :D 1 - well, clearly insufficient. 2 - AB+CD=BC+DA - it might be a rectangle or a square, in which all sides are equal. not sufficient.

1+2 - it might be a square, or a quadrilateral consisting of 2 triangles, 2 small and 2 big right triangles 30-60-90, with hypotheses equal to each other. so insufficient.

Re: If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

03 Nov 2015, 08:26

mvictor wrote:

damn, please mention that the diagonals are perpendicular. I was thinking, how the hell can 2 different sides be perpendicular to each other? :D 1 - well, clearly insufficient. 2 - AB+CD=BC+DA - it might be a rectangle or a square, in which all sides are equal. not sufficient.

1+2 - it might be a square, or a quadrilateral consisting of 2 triangles, 2 small and 2 big right triangles 30-60-90, with hypotheses equal to each other. so insufficient.

It is given that ABCD is a quadrilateral and as AC is perpendicular to BD, it is implied that diagonals are perpendiculars. This is the usual interpretation. Why do you need it to be mentioned explicitly that "diagonals are perpendicular"?

Re: If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

03 Nov 2015, 08:32

Engr2012 wrote:

mvictor wrote:

damn, please mention that the diagonals are perpendicular. I was thinking, how the hell can 2 different sides be perpendicular to each other? :D 1 - well, clearly insufficient. 2 - AB+CD=BC+DA - it might be a rectangle or a square, in which all sides are equal. not sufficient.

1+2 - it might be a square, or a quadrilateral consisting of 2 triangles, 2 small and 2 big right triangles 30-60-90, with hypotheses equal to each other. so insufficient.

It is given that ABCD is a quadrilateral and as AC is perpendicular to BD, it is implied that diagonals are perpendiculars. This is the usual interpretation. Why do you need it to be mentioned explicitly that "diagonals are perpendicular"?

IDK, I just spent additional seconds trying to figure out wtf is actually meant

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If ABCD is a quadrilateral, is AB=BC=CD=DA ?

(1) AC is perpendicular to BD (2) AB+CD=BC+DA

There are 5 variables (4 sides, 1 diagonal) in a quadrilateral, so we need 5 equations in order to solve the question, but only 2 equations are given from the 2 conditions, so there is high chance (E) will be our answer. Even if we combine the 2 conditions together, they are insufficient, so (E) becomes the answer.

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________

Re: If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

17 Apr 2017, 11:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If ABCD is a quadrilateral, is AB=BC=CD=DA ? [#permalink]

Show Tags

07 Sep 2017, 21:13

tt11234 wrote:

If ABCD is a quadrilateral, is AB=BC=CD=DA ?

(1) AC is perpendicular to BD (2) AB+CD=BC+DA

There's simply not enough because two diagonals being perpendicular does not mean the same thing as those diagonals being perpendicular bisectors. Bunuel am I right? Because if all we know is that two diagonals are perpendicular then the quadrilateral could be a kite, which graphically makes a lot of sense. However, if we know that the two diagonals bisect eachother, or more precisely are perpendicular bisectors, then we know for sure that that quadrilateral is a rhombus because the definition of a perpendicular bisector simply means cutting a quadrilateral into two equal pieces at 90 degrees. And that furthermore every square is a rhombus but not all rhombuses are squares?

There's simply not enough because two diagonals being perpendicular does not mean the same thing as those diagonals being perpendicular bisectors. Bunuel am I right? Because if all we know is that two diagonals are perpendicular then the quadrilateral could be a kite, which graphically makes a lot of sense. However, if we know that the two diagonals bisect eachother, or more precisely are perpendicular bisectors, then we know for sure that that quadrilateral is a rhombus because the definition of a perpendicular bisector simply means cutting a quadrilateral into two equal pieces at 90 degrees. And that furthermore every square is a rhombus but not all rhombuses are squares?

A rhombus is a quadrilateral with all sides equal in length. A square is a quadrilateral with all sides equal in length and all interior angles right angles.

Thus a rhombus is not a square unless the angles are all right angles. A square however is a rhombus since all four of its sides are of the same length.
_________________