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

 It is currently 09 Dec 2018, 21:09

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# A rectangular circuit board is designed to have width w inches, perime

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 30 May 2005
Posts: 271
A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

Updated on: 06 Nov 2018, 02:39
2
5
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:29) correct 31% (01:46) wrong based on 883 sessions

### HideShow timer Statistics

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) $$w^2 + pw + k = 0$$

(B) $$w^2 – pw + 2k = 0$$

(C) $$2w^2 + pw + 2k = 0$$

(D) $$2w^2 – pw – 2k = 0$$

(E) $$2w^2 – pw + 2k = 0$$

Originally posted by mandy on 14 Jun 2005, 07:55.
Last edited by Bunuel on 06 Nov 2018, 02:39, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

25 Jul 2013, 02:29
4
2
mandy wrote:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.

Now, assume:
Width = w = 1 inch and length = 1 inch;
Perimeter = p = 4 inches;
Area = k = 1 square inches.

Plug the values of w, p, and k into the answer choices: only for E 2w^2 - pw + 2k = 2 - 4 + 2 = 0.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
_________________
Senior Manager
Joined: 17 Apr 2005
Posts: 354
Location: India
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

14 Jun 2005, 10:40
5
2
mandy wrote:
. Hello
need help thanks
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?
(A) w^2+pw+k=0
(B) w^2-pw+2k=0
(C) 2 w^2+pw+2k=0
(D) 2 w^2-pw-2k=0
(E) 2w^2-pw+2k=0

Another way to solve the problem is to choose a rectangle of your own.

I chose one , in which each side was 1 unit.
hence w =1 , p =4 and k = 1.

Only E satisfied these values.

HMTG.
##### General Discussion
Manager
Joined: 28 Sep 2004
Posts: 79
Location: New York City
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

14 Jun 2005, 08:04
1
mandy wrote:
. Hello
need help thanks
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?
(A) w^2+pw+k=0
(B) w^2-pw+2k=0
(C) 2 w^2+pw+2k=0
(D) 2 w^2-pw-2k=0
(E) 2w^2-pw+2k=0

C :

K = [(P-2W)/2] *W
thus 2k = PW - 2W^2
= 2w^2 - PW + 2k = 0
Intern
Joined: 26 Sep 2012
Posts: 15
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

25 Jul 2013, 02:18
1
mandy wrote:
. Hello
need help thanks
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?
(A) w^2+pw+k=0
(B) w^2-pw+2k=0
(C) 2 w^2+pw+2k=0
(D) 2 w^2-pw-2k=0
(E) 2w^2-pw+2k=0

Let l be the length of the board, then p = 2l + 2w, k = w*l
By plugging, we can find that the answer is E:
$$2w^2 - w(2l + 2w) + 2w*l = 0$$, thus
2w - 2l - 2w + 2l = 0
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

25 Jul 2013, 02:24
mandy wrote:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

Similar question to practice: an-equilateral-triangle-is-inscribed-in-a-circle-if-the-130556.html
_________________
Moderator
Joined: 21 Jun 2014
Posts: 1089
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

09 Apr 2016, 09:24
1
mandy wrote:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

lets say length is X.

area K = WX, hence X= K/W
perimeter P = 2W+2X

P = 2W + 2K/W
PW = 2W^2 + 2K

2w^2 - pw + 2k = 0 -- E
_________________

---------------------------------------------------------------
Target - 720-740
Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

11 Oct 2017, 00:24
1
Let x = length
p=2w+2x ===> x=1/2p-w

k=wx ===> x=k/w

Substituting:

k/w=1/2p-w
k=1/2pw-w^2
2w^2-pw+2k=0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

28 Nov 2017, 04:56
2
mandy wrote:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

Let's see how the 3 are related.

Perimeter = 2*(Length + Width)
(p - 2w)/2 = Length

Area = Length * Width
k = (p - 2w)/2 * w
2k = pw - 2w^2
2w^2 - pw + 2k = 0

_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4261
Location: United States (CA)
Re: A rectangular circuit board is designed to have width w inches, perime  [#permalink]

### Show Tags

29 Nov 2017, 17:13
mandy wrote:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

(A) w^2 + pw + k = 0
(B) w^2 - pw + 2k = 0
(C) 2w^2 + pw + 2k = 0
(D) 2w^2 - pw - 2k = 0
(E) 2w^2 - pw + 2k = 0

We can let n = the length of the rectangle and create the following equation:

2w + 2n = p

2n = p - 2w

n = (p - 2w)/2

Since area = n x w:

k = (n)(w)

k = [(p - 2w)/2]w

2k = pw - 2w^2

2w^2 - pw + 2k = 0

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: A rectangular circuit board is designed to have width w inches, perime &nbs [#permalink] 29 Nov 2017, 17:13
Display posts from previous: Sort by