This Weeks MGMAT problem

my bad G, i made an error

Where is it given in the question AB = AC ?

you are right, its not given.

From 2, can't we determine the areas of both objects in terms of AC?

We can indeed. I vote B.

The circle and the square are both ((AC)^2)/2

Stoofi,

You are assuming that the quadrilateral is sqare. That can not be said from 2nd statment alone. Try to draw a quadrilateral with equal diagonals but sucha that it is not square.

Nope. I am assuming that that it's a parallelogram, or a rhombus, I think...

For which quadrilaterals does the area= D1*D2 *.5 work?

I believe this formula is for SQUARE only. Assume that x is the side of a square. Theb x^2 + x^2 = D1^2 => 2x^2 = D1^2 => x^2 = D1^2 / 2
=> x^2 = D1* D1 / 2 => Area = D1 * D2 * 0.5

Yep. I'm wrong. That formula works for squares and rhombuses, but not for all rectangles.

Based on all the discussion, is "C" the final answer?

vote for C too.
from A: sides are equal. we don't know whether it is a sq. or a rhombus
from B: diagonals are equal. sq. or a rectangle.

combine A and B. it is a square.

dj,

you are right . i am having a bad day.

thanks
praetorian

I am not sayin' that side equals diagonal. but, when sides are equal and diagonals are equal, it has to be a square.

My guess is D.

(1) If ABCD is a square then we have AreaOfSquare = AreaOfCircle. Same thing even if ABCD is a rhombus.
(2) AC = XY*sqrt(2PI)
AC┬▓ = 2PI(XY┬▓)
AC┬▓/2 = PI*XY┬▓
AreaOfSquare = AreaOfCircle

here you assume that the QUAD is a square. that not correct.

We must know either
1. that the diagonals are equal
2. the angles are 90.

as you say, it can be a rhombus too , then what?
A = 1/2 d1 d2
how you gonna find d1 d2?





again, you assume upfront that the QUAD is a square.
just because you get AC^2/2 , that does not mean that the QUAD is a square, does it?


Dj said it right.

from 1 and 2, the QUAD can only be a square.
ok...so we settled the shape issue.


We could stop right here..since we know the question can be answered..And we get C.

but just for giggles.

Now, the area of the QUAD is just AB^2 , which is just the area of a
square.
From 1, we have XY = AB / sqrt(PI)

So the area of circle = PI * AB^2 / PI = AB^2

voila, The answer is yes


thanks
praetorian

Hey you guys can settle with any answer you want... your choice!

what do we have here... a stranded square or a rooted answer C ??