Bunuel wrote:

In the diagram above what is the length of MP if LNOQ is a square with an area of 64?

(1) a - b = 0

(2) OP = OQ/2

Attachment:

2018-03-13_1822_001.png

As we're asked to assess the length of MP, we'll try playing with the figure.

This is an Alternative approach.

The shortest MP can be is if it is a straight line, that is parallel to LQ.

The longest MP can be is if it is a diagonal of a square.

We'll try drawing MP so it is as long or as short as possible.

(1) if a = b = 90 then MP is a straight line and if a = b = 45 MP is a diagonal.

Insufficient.

(2) We now know the exact location of point P but can still move point M around giving different lengths.

Insufficient.

Combined.

We know the exact location of point P but can still move point M around.

(Is MP a straight line or does it have a slope? Either way a =b as the sides of the square are parallel)

Insufficient!

(E) is our answer.

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