GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Feb 2019, 18:02

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• Free GMAT practice

February 15, 2019

February 15, 2019

10:00 PM EST

11:00 PM PST

Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need.

The vertex of the square MNOP is located at the center of circle O. If

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52905
The vertex of the square MNOP is located at the center of circle O. If  [#permalink]

Show Tags

05 Feb 2018, 05:41
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:14) correct 15% (01:35) wrong based on 52 sessions

HideShow timer Statistics

The vertex of the square MNOP is located at the center of circle O. If arc NP is $$4\pi$$ units long, then which of the following is the perimeter of the square MNOP ?

(A) 32

(B) $$32\pi$$

(C) 64

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:

2018-02-05_1739.png [ 10.3 KiB | Viewed 858 times ]

_________________
Director
Joined: 06 Jan 2015
Posts: 586
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: The vertex of the square MNOP is located at the center of circle O. If  [#permalink]

Show Tags

05 Feb 2018, 05:51
Bunuel wrote:

The vertex of the square MNOP is located at the center of circle O. If arc NP is $$4\pi$$ units long, then which of the following is the perimeter of the square MNOP ?

(A) 32

(B) $$32\pi$$

(C) 64

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:
2018-02-05_1739.png

Arc length = $$2\pi$$r(center angle/360)

Here $$4\pi$$=$$2\pi$$r(90/360)

r=8

Perimeter =32

Hence A
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Senior SC Moderator
Joined: 22 May 2016
Posts: 2464
Re: The vertex of the square MNOP is located at the center of circle O. If  [#permalink]

Show Tags

05 Feb 2018, 12:12
Bunuel wrote:

The vertex of the square MNOP is located at the center of circle O. If arc NP is $$4\pi$$ units long, then which of the following is the perimeter of the square MNOP ?

(A) 32

(B) $$32\pi$$

(C) 64

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:
The attachment 2018-02-05_1739.png is no longer available

Attachment:

2018-02-05_1739.ed.png [ 20.89 KiB | Viewed 603 times ]

Length of arc NP = $$4π$$
Arc length is a fraction of circumference.
Derive that fraction from central angle/circle angle.
From circumference, derive radius, which equals side length of the square.

• Arc length = fraction of circumference

To find that fraction, we need the central angle of sector NOP
A sector's arc length is the portion of the circumference that is subtended by sector's central angle.

• Central angle of sector NOP?

Square MNOP has a vertex located at center O
A square's vertex = 90°
Hence the central angle of sector NOP = 90°

• Sector NOP as a fraction of the circle?

$$\frac{Part}{Whole}=\frac{SectorAngle}{360}=\frac{90}{360}=\frac{1}{4}$$

•Circumference of circle?

Sector NOP's arc = $$\frac{1}{4}$$ of circumference
Length of arc NP = 4π
4π = $$\frac{1}{4}$$ circumference
Circumference = 16π

Circumference = $$2πr = 16π$$
$$r = 8$$
$$r = s$$
, side of square
$$s = 8$$

• Perimeter of square? $$= 4s$$
$$4s = 4 * 8 = 32$$

_________________

To live is the rarest thing in the world.
Most people just exist.

Oscar Wilde

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: The vertex of the square MNOP is located at the center of circle O. If  [#permalink]

Show Tags

06 Feb 2018, 17:03
Bunuel wrote:

The vertex of the square MNOP is located at the center of circle O. If arc NP is $$4\pi$$ units long, then which of the following is the perimeter of the square MNOP ?

(A) 32

(B) $$32\pi$$

(C) 64

(D) $$64\pi$$

(E) $$72\pi$$

Attachment:
2018-02-05_1739.png

Since arc NP is 4π, and 4π corresponds to a 90 degree central angle, then 4π is 90/360 = 1/4 of the circumference of the circle.

Thus, the circumference is 4π x 4 = 16π. Thus, the diameter is 16, and the radius is 8.

So, side NO = side of square = radius = 8, and the perimeter of the square is 8 x 4 = 32.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: The vertex of the square MNOP is located at the center of circle O. If   [#permalink] 06 Feb 2018, 17:03
Display posts from previous: Sort by