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# This Weeks MGMAT problem

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CEO
Joined: 15 Aug 2003
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Kudos [?]: 703 [0], given: 781

This Weeks MGMAT problem [#permalink]  15 Dec 2003, 02:55
in other words, Is Area of Quad = Area of circle?

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.
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
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Kudos [?]: 27 [0], given: 0

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.
Senior Manager
Joined: 05 May 2003
Posts: 427
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

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.
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 703 [0], given: 781

Last edited by Praetorian on 15 Dec 2003, 23:46, edited 1 time in total.
Senior Manager
Joined: 05 May 2003
Posts: 427
Location: Aus
Followers: 2

Kudos [?]: 5 [0], given: 0

praetorian123 wrote:
Geethu wrote:
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 ?
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 703 [0], given: 781

Geethu wrote:
praetorian123 wrote:
Geethu wrote:
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.
Director
Joined: 28 Oct 2003
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Location: 55405
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Kudos [?]: 10 [0], given: 0

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
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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stoolfi wrote:
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.
Director
Joined: 28 Oct 2003
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Location: 55405
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Kudos [?]: 10 [0], given: 0

Quote:
You are assuming that the quadrilateral is sqare

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?
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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Kudos [?]: 0 [0], given: 0

stoolfi wrote:
Quote:
You are assuming that the quadrilateral is sqare

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
Director
Joined: 28 Oct 2003
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Kudos [?]: 10 [0], given: 0

Yep. I'm wrong. That formula works for squares and rhombuses, but not for all rectangles.
Manager
Joined: 06 Jun 2003
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Kudos [?]: 1 [0], given: 0

Based on all the discussion, is "C" the final answer?
Director
Joined: 13 Nov 2003
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Location: Florida
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Kudos [?]: 32 [0], given: 0

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.
CEO
Joined: 15 Aug 2003
Posts: 3469
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Kudos [?]: 703 [0], given: 781

dj wrote:
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

Last edited by Praetorian on 15 Dec 2003, 23:48, edited 1 time in total.
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 32 [0], given: 0

praetorian123 wrote:
dj wrote:
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.
Manager
Joined: 26 Aug 2003
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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
CEO
Joined: 15 Aug 2003
Posts: 3469
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Kudos [?]: 703 [0], given: 781

wonder_gmat wrote:
My guess is D.

Quote:
(1) If ABCD is a square then we have AreaOfSquare = AreaOfCircle. Same thing even if ABCD is a rhombus.

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?

Quote:
(2) AC = XY*sqrt(2PI)
AC┬▓ = 2PI(XY┬▓)
AC┬▓/2 = PI*XY┬▓
AreaOfSquare = AreaOfCircle

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

thanks
praetorian
Manager
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praetorian123 wrote:
We could stop right here..since we know the question can be answered..And we get C.

Hey you guys can settle with any answer you want... your choice!
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 32 [0], given: 0

wonder_gmat wrote:
praetorian123 wrote:
We could stop right here..since we know the question can be answered..And we get C.

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 ??
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