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IS quadrilateral MNOP a square?

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IS quadrilateral MNOP a square?

by bpolley00 » Fri Jun 07, 2013 8:56 am
IS quadrilateral MNOP a square?
1)MN=NO=OP
2) Angle N and Angles O are right Angles

Question in regard to this question: isn't it a matter of how you label Quadrilateral MNOP? For example- If you make the quadrilateral and label the 4 points M and N at the top and P and O at the bottom then you come up with the answer E. However, if you label the two top points M O and the bottom N P, you come up with C as it depends on how the right angles are allocated on the quadrilateral.

Thoughts?
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by ceilidh.erickson » Fri Jun 07, 2013 11:23 am
To a certain extent, you're right - it depends on how the angles are labeled. If angle N and angle O are opposite each other, it would have to create a rectangle. If, however, N and O are next to each other, we could have a trapezoid (see diagram below).

Image

Generally speaking, the GMAT will label vertices in alphabetical order, but you're right - we can't assume that.

However... if MN = NO = OP, then the trapezoid scenario that we drew above is impossible. It would be possible to have a trapezoid in which MN = NO = MP, and OP was a different length. But if the three equal sides are all of the sides that touch the 90 degree angles of N and O, there's no way for that 4th side not to be equal as well.

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by fcabanski » Fri Jun 07, 2013 12:13 pm
The name defines where the letters go in the figure. Since it is named MNOP, the vertices are in order M, N, O, P.

Anticipate the needed info. For geo figures, angles describe shape and side length describes size. For an object to be a square it needs four 90 degree angles, and four sides of equal length.

If three of the angles are 90 degrees, the fourth one has to be 90. The sum of the interior angles of a quad is 360.


Evaluate the statements:

1: Three sides are equal. The fourth side can be any length. This is not sufficient. Eliminate A and D. The possible answers are B, C and E.

2: Two angles are 90 degrees. The sum of the other two angles has to be 180, but the angles could be 170 and 10, or any combo equaling 180. This is not sufficient. Eliminate B. Only C and E remain.

Are 1 and 2 together sufficient? (C): The only way side MP closes the figure (it is closed since the question indicates it is a quadrilateral) is if MP is equal to the other three sides. If it's shorter, then the figure isn't a quadrilateral. If it's longer then it overhangs the opposite side, and the figure isn't a quadrilateral. Similarly, the only way it touches the end of MN is if angle P is right. If P, N and O are right, then M is right (sum of angles = 360). This is sufficient.

C is the answer.
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by bpolley00 » Fri Jun 07, 2013 2:05 pm
Professor Erickson,

That was a great response. See that is where I got tripped up, I knew that all 3 lines had to be the same length but I figured the fourth line, MP, could still be used to create a trapezoid. This test has so many minute parts to each question and as you can tell I am not going to leave here until I get a 700+. Although, I just started looking at things again. Thanks for your help.

Also, wasn't ignoring you fcabanski, her answer just directly solved my problem. Thanks for your help!

Sincerely

-BP
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by fcabanski » Fri Jun 07, 2013 11:38 pm
Make sure you don't get confused with naming. If the quadrilateral is named MNOP, the vertices cannot be in any random order. They must be in order MNOP - wherever you start with M, N is next, then O, then P.

The rectangle drawn in an earlier post is not MNOP. It's MNPO.
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by hemant_rajput » Sat Jun 08, 2013 10:33 am
fcabanski wrote:
2: Two angles are 90 degrees. The sum of the other two angles has to be 180, but the angles could be 170 and 10, or any combo equaling 180. This is not sufficient. Eliminate B. Only C and E remain.
if the adjacent angle of any quadrilateral are equal to 90 each then other two angle has to be of 90 degree. Supplementary angles are always equal to 90. Now why 2nd statement is not sufficient because this quad can be rectangle or it can square.

therefore you need both 1 and 2 to answer the question.

Please correct me if I'm wrong
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by fcabanski » Sat Jun 08, 2013 2:35 pm
"If the adjacent angle of any quadrilateral are equal to 90 each then other two angle has to be of 90 degree."

That's not true.

Image

"Supplementary angles are always equal to 90."

That's not true. The sum of supplementary angles is 180 degrees. The angles could be 10 and 170, or 140 and 40, or any two angles with a sum of 180 degrees.

The solution I wrote indicated C, both together are sufficient, is the answer.
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