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This Weeks MGMAT problem [#permalink]
15 Dec 2003, 02:55

in other words, Is Area of Quad = Area of circle?

My Answer : C

1. it could be square or a rhombus. (equal sides)
note that AB ^2 = PI * XY^2
in other words, if this figure is a square, we are done.. but from 1, we cant say for sure.

2. it could be a square or a rectangle. ( diagonals equal)
here AC^2 = 2* (PI) * XY^2
not sufficient , one would think

combine, we can say definitely that the figure is a square.
and from 1, we know that area of square = area of circle

i get C

thanks
praetorian

Last edited by Praetorian on 15 Dec 2003, 23:44, edited 4 times in total.

I think it should be E. from both we can assume that it is a square, but what is the lenght of the side of this square? Is it XYsqroot(pi) or it is when we use the diagonal as equal to XYsqroot(pi) and find the side? Because in this cases the square has different areas and we can not determine the amount of paint used.

I am also getting C as answer. But, I feel each mural will require same amount of paint. I did it in the following way. Assume AB = a = XY root(pi) Area of the square = a power 2 = (XY) power 2 * pi Area of the circle = pi (r) power 2 = (XY) power 2 * pi Both are equal.

Its not a square. analyze both statements again.

Where is it given in the question AB = AC ?

you are right, its not given.

Last edited by Praetorian on 15 Dec 2003, 23:47, edited 1 time in total.

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

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.

you missed it too. from 1 and 2, we get AB = AC ( both AB and AC are equal to sqrt(PI) * XY and thus AB and AC equal to each other) AB is the side of the QUAD and AC is the diagonal of the QUAD. in a square, side is not equal to the diagonal. So the QUAD cant be a square.

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.

(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