Is quadrilateral q a rhombus?

Question

(1) Quadrilateral q has four equal sides
(2) Quadrilateral q has four equal angles

Bunuel · Answer

Is quadrilateral q a rhombus?

Definition: rhombus is a quadrilateral with all four sides equal in length.

(1) Quadrilateral q has four equal sides --> quadrilateral q is a rhombus. Sufficient.

(2) Quadrilateral q has four equal angles. Quadrilateral q could be a rectangle (which is not a square, thus not a rhombus) as well as a square, thus a rhombus. Not sufficient.

Answer: A.

For more on Polygons check: math-polygons-87336.html

Hope it helps.

Simba2012 · Answer

Bunuel
 But a square can also have all equal sides so how can statement A is sufficient?

Bunuel · Answer

All squares are rhombuses, thus if q is a square then it's a rhombus too.

Nunuboy1994 · Answer

Is quadrilateral q a rhombus?

(1) Quadrilateral q has four equal sides
(2) Quadrilateral q has four equal angles

Statement (1) tells us that the quadrilateral has four equal sides and is thus a rhombus. A rhombus is essentially an equilateral parallelogram. Also,  all  squares are rhombuses but not all rhombuses are squares. Sufficient.

Statement (2) tells us that the quadrilateral has four equal angles- though, a rectangle also has four equal angles and doesn't necessarily have to four equal sides unless it is square- which there is still not enough information to deduce. Insufficient.

A

KrishnakumarKA1 · Answer

the property for the rhombus is all four side is equal and the diagonal bisect each other at right angle.

St 1: SUFFICIENT
ST 2: INSUFFICIENT as the quadrilateral might be rectangle or a square. INSUFFICIENT

Option A

ShankSouljaBoi · Answer

Recently saw your video on kite properties. You have erroneously mentioned in the video that both the diagnols in a kite are perpendicular bisectors. I wasted an hour because of this, please amend.

dcummins · Answer

For clarity. On the GMAT we don't differentiate between a square and a rhombus specifically?

Bunuel · Answer

We do.

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.

So, all squares are rhombi but not all rhombi are squares.

rprashar · Answer

shouldn’t it be a parallelogram with equal sides rather than just quadrilateral.

Posted from my mobile device

bumpbot · Answer

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.

Is quadrilateral q a rhombus?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is quadrilateral q a rhombus?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards