Circle and Rectangle's areas

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Sep 14, 2013 11:53 pm

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

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Source: Beat The GMAT — Data Sufficiency | Sat Sep 14, 2013 11:53 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 15, 2013 12:01 pm

Hi gmmattesttaker2,

For these types of questions, it helps to draw pictures and TEST values. I'm going to give you some "nudges" so that you can try this question again.

Here, we're told that a circle is drawn within a rectangle. The question: "Is the circle MORE than 1/2 of the rectangle's AREA?"

Fact 1 tells you the rectangle's length is > 2(width)

Nudge: DRAW a rectangle. TEST a number for the length and the width that fits this given info. Next, think about the BIGGEST circle that you could draw in this rectangle. By definition, the diameter of this circle can't be any bigger than the width of the rectangle. So what does that mean about the two areas???

Fact 2 different info about the rectangle, but the same tactics apply.

Nudge: Draw your pictures using the given info and compare the areas.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Sep 16, 2013 3:21 am

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

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Mon Sep 16, 2013 12:53 pm

Dear gmattesttaker2,

It looks as if you have gotten some very good responses from both Rich and rahulmittal87.

I will just add --- decreasing each length by 25% means that we are multiplying by a scale factor of 0.75 = 3/4. The resultant change in area would be proportion to the square of the scale factor --- (3/4)^2 = 9/16, which only slightly bigger than 1/2. When we shrink each length by 25%, we wind up with a rectangle that is little more than half the original area. See:
https://magoosh.com/gmat/2012/scale-fact ... decreases/

Let me know if you have any further questions.
Mike

Magoosh GMAT Instructor
https://gmat.magoosh.com/

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Mon Sep 16, 2013 9:48 pm

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.

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Mon Sep 16, 2013 9:53 pm

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

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Sep 16, 2013 9:54 pm

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.

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Sep 16, 2013 9:58 pm

If i were using those values, then my assumptions would fail in the Statement one itself.

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

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Mon Sep 16, 2013 10:00 pm

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.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Sep 16, 2013 10:03 pm

You are welcome

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.

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