gmattesttaker2 wrote:Hello,

Can you please assist with this? This is from MGMAT:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle's area?

(1) The rectangle's length is more than twice its width.

(2) If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.


OA: D

rahulmittal87 wrote:

gmattesttaker2 wrote:Hello,

Can you please assist with this? This is from MGMAT:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle's area?

(1) The rectangle's length is more than twice its width.

(2) If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.


OA: D

Let's solve by assuming values for L & B of rectangles as 20 & 10.
Statement 1:
Area of Rectangle = 20 x 10 = 200
Maximum possible area of circle that can be inscribed in rectangle is : 3.14 x (5) x (5) = Say just more than 75.
So SUFFICIENT
Statement 2:
New length = 15
New Breadth = 10 x 3/4
New Area = 15 x 10 x 3/4 = say around 112
Maximum possible area of circle that can be inscribed in rectangle is : 3.14 x (5 x 3/4)^2 = around 45
SUFFICIENT
HENCE, D

Uva@90 wrote:Hi All,

I am confused with the question and the answer given.

Here is what I understood and how I solved,
Question ask us to find does circle area is more than one half of the rectangular area ?

Before proceeding to the statements I understood we need to know Radius of the circle, length and width of the rectangle.

Statement1: Rectangle length is more than twice of its width.

It did not state anything about the Radius. So radius can be anything.
Hence, Insufficient.

Statement2: If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.

Again It didn't say anything about radius. So insufficient.

I choosed OA as E

Experts & Friends
Please Help me where I went wrong.

Thanks in advance.

Regards,
Uva.

Uva@90 wrote:

rahulmittal87 wrote:

gmattesttaker2 wrote:Hello,

Can you please assist with this? This is from MGMAT:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle's area?

(1) The rectangle's length is more than twice its width.

(2) If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.


OA: D

Let's solve by assuming values for L & B of rectangles as 20 & 10.
Statement 1:
Area of Rectangle = 20 x 10 = 200
Maximum possible area of circle that can be inscribed in rectangle is : 3.14 x (5) x (5) = Say just more than 75.
So SUFFICIENT
Statement 2:
New length = 15
New Breadth = 10 x 3/4
New Area = 15 x 10 x 3/4 = say around 112
Maximum possible area of circle that can be inscribed in rectangle is : 3.14 x (5 x 3/4)^2 = around 45
SUFFICIENT
HENCE, D

Hi Rahul,

Why don't you consider rectangle of Length 10 and width 20 ?

Regards,
Uva

rahulmittal87 wrote:Uva, the question says:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle's area?

So the circle cannot come outside the rectangle. Hence, the radius cannot be larger than the half of the smallest side of the rectangle.

Uva@90 wrote:Hi All,

I am confused with the question and the answer given.

Here is what I understood and how I solved,
Question ask us to find does circle area is more than one half of the rectangular area ?

Before proceeding to the statements I understood we need to know Radius of the circle, length and width of the rectangle.

Statement1: Rectangle length is more than twice of its width.

It did not state anything about the Radius. So radius can be anything.
Hence, Insufficient.

Statement2: If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.

Again It didn't say anything about radius. So insufficient.

I choosed OA as E

Experts & Friends
Please Help me where I went wrong.

Thanks in advance.

Regards,
Uva.

Uva@90 wrote:

rahulmittal87 wrote:Uva, the question says:

A circle is drawn within the interior of a rectangle. Does the circle occupy more than one-half of the rectangle's area?

So the circle cannot come outside the rectangle. Hence, the radius cannot be larger than the half of the smallest side of the rectangle.

Uva@90 wrote:Hi All,

I am confused with the question and the answer given.

Here is what I understood and how I solved,
Question ask us to find does circle area is more than one half of the rectangular area ?

Before proceeding to the statements I understood we need to know Radius of the circle, length and width of the rectangle.

Statement1: Rectangle length is more than twice of its width.

It did not state anything about the Radius. So radius can be anything.
Hence, Insufficient.

Statement2: If the rectangle's length and width were each reduced by 25% and the circle unchanged, the circle would still fit into the interior of the new rectangle.

Again It didn't say anything about radius. So insufficient.

I choosed OA as E

Experts & Friends
Please Help me where I went wrong.

Thanks in advance.

Regards,
Uva.

AHhh Rahul Correct I forget that Circle radius cant be more than half of the smallest side of the rectangle.

Thanks dude.

Regards,
Uva.