Is quadrilateral MNOP a square?

For (1) MNOP may or may not be a square as shown below:Hope it helps
_________________

St1: Just two of the many different possibilities are : Rhombus and Square. Insuff
St2: Just two of the many different possibilities are : Rectangle and Square. Insuff

St1+St2: It could only be square
Ans: C

This one looks so easy you might think there is a trap; definitely C.

So true, I was wondering what would the diagram look like for statement 1...

It does help, thank you; Visual aids like this one will be very helpful under stressful and timed conditions when one might momentarily confuse a general quadrilateral with a square specifically. Remembering this drawings will definitely help!

Stupid, annoying question (sorry, I just had to vent):

1) tells us the lengths of three sides but this theoretically still could leave us with a fourth side that is longer/shorter than the rest, so insufficient

2) Tells us that our quadrilateral is either a rectangle or a square, insufficient.

1 + 2 tell us that our quadrilateral is a square, because 2) restricts the possible shapes that 1) can take, and combining the two tells us how long the fourth side in 1) is, so sufficient.

C

Found this question interesting cause my mind wanted to complicate it...Might sound dumb but is it a given in Math to assume that MNOP is in order? Wouldn't it change things if M and N were on a diagonal?

Hi
yes, the alphabets give us the order of vertices
_________________

Hi raviraaj,

We always read the vertices in the order (Clockwise or Anticlockwise) of their placements and don't consider them random vertices.


... And no question is dumb question it's more of exposure and less of competence that makes a difference among the level the questions test takers ask. SO don't be shy in asking any question however dumb you feel about that question.

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

Hope it helps.
_________________

Bunuel how do we know from statement 2 that MNOP must be a rectangle or square?

Why can we not have a right trapezoid based on statement 2?

It does not have to be a square or a rectangle, it might also be a right trapezoid.
_________________

Hi guys,

Is it correct that, according to Statement 1), it could be a rhombus?
_________________

Hi ghnlrug

A rhombus becomes a square if the angles are 90 degree. What you wrote is true if the fourth side is also equal. It could be a rhombus.

For more on the theory check this link

https://gmatclub.com/forum/math-polygons-87336.html

Posted from my mobile device

No. No necessary as the 4th side of the quadrilateral need not be equal to other three.

Posted from my mobile device

So, in other words, YES
_________________

Hi, could this be a complex quad (with intersecting sides)?

@

Hi Bunuel,
I didn't understand that if the stem says it's a quadrilateral and not a parallelogram than how can we say that if two angles are 90 and three sides are equal, it's a square.

I'm confused with that. Can you please explain in detail.

Vinay

We know the 4 sides are in the order: M, N, O, P.

IF M and O are right angles, along with statement 1, we can conclude MNOP is a square. Without statement 1, it's possible that MNOP is a rectangle.

_________________