If vertex P in square PQRS is pinned and square PQRS is rotated clock

Question

If vertex P in square PQRS is pinned and square PQRS is rotated about vertex P, what is the number of degrees the square must be rotated until the first time that vertex Q will be in the position where vertex S is now? 
A) 45 
B) 90 
C)135 
D)180 
E) 270

Abhishek009 · Answer

Clean (B) 90 Original picture - PQRS 1.jpg After 90 degree clockwise rotation - PQRS 2.jpg PS : Pardon me , the square doesn't look like a square it seems more like a rectangle.

generis · Answer

squarerotate.jpg Abhishek009 - I think the answer depends on how you label the square. Typically, the easiest way to solve vertex rotation questions is to inscribe them in a circle if possible . . . I get (90° + 90°) = 180° ANSWER D sqrotate.jpg

pandeyashwin · Answer

Answer should be option D 180

swagatamoitra · Answer

I think the question is ambiguous in the sense that how you label the square will determine the answer. So to avoid it please add a picture of a labelled square as per the question desires. Else there can be two answers as pointed out by people in above posts and it will be a waste of everyone's time to attempt it.

GMATBusters · Answer

Hi The square is hinged at vertex P. But you have considered the hinge at centre. Considering the centre of rotation as vertex P, answer will be 90 deg. See the sketch. IMG_20180703_163515.jpg

GMATBusters · Answer

Hii

Square PQRS means that P, Q,R,S are adjacent vertices.

Also please note that square is hinged at vertex P.
See my post for explanation.

GMATBusters · Answer

swagatamoitra

Figure/picture of Square PQRS is not required

To name a polygon, list its vertices in order as you move around it in either direction.

Attachment:

IMG_20180703_171604.jpg [ 15.35 KiB | Viewed 2543 times ]

See the figure. One name for the shaded triangle is Triangle ABC. Other names are possible, including BCA and ACB. One name for the white triangle is Triangle ADC.

The quadrilateral in the figure could be named Quadrilateral ABCD, BCDA, DCBA, or DABC. All of these names list the vertices in order as you move around the quadrilateral. The name ACBD is not correct.

generis · Answer

Since I answered the question originally, the phrasing has changed. Original wording: New wording: "Clockwise" has been removed. I may be mistaken, but it seems as if we have two answers . If we rotate the square on the pivot point of P in one direction, as in my diagram below, the answer is 90° If we were to rotate the square on the pivot point of P in the other direction, the answer would be 270° (In case there is confusion about the discussion of labeling vertices . . . Originally, vertices labeled out of alphabetical order were acceptable. As clarified by the author above, vertices may not be labeled out of alphabetical order.) I do not quite understand the diagram drawn by gmatbusters , so I drew my own. My diagram and that by gmatbusters may well be identical, but "in the same position" is clarified in my diagram. If "in the same position" means "directly below vertex P," and if we rotate the square about the anchor point P in the same direction as I did below , then I suspect this depiction is the way to explain an answer of 90° qqqqqqqqq.jpg

GMATBusters · Answer

Hi  Abhishek009

You have drawn the Square incorrectly.

The vertices must be in the same order as the order of the Name of Polygon.

You have drawn Square PQSR or QSRP or SRPQ or RPQS but NOT PQRS.

Any polygon ( of n sides) can be name in "n" number of ways.

If vertex P in square PQRS is pinned and square PQRS is rotated clock

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If vertex P in square PQRS is pinned and square PQRS is rotated clock

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