Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 30 May 2005
Posts: 274

A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
14 Jun 2005, 07:55
1
This post received KUDOS
8
This post was BOOKMARKED
Question Stats:
69% (01:30) correct 31% (01:46) wrong based on 835 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
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 25 Jul 2013, 02:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Manager
Joined: 28 Sep 2004
Posts: 80
Location: New York City

Re: ps CIRCUIT BOARD [#permalink]
Show Tags
14 Jun 2005, 08:04
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^2pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2pw2k=0 (E) 2w^2pw+2k=0
C :
K = [(P2W)/2] *W
thus 2k = PW  2W^2
= 2w^2  PW + 2k = 0



Senior Manager
Joined: 17 Apr 2005
Posts: 372
Location: India

Re: ps CIRCUIT BOARD [#permalink]
Show Tags
14 Jun 2005, 10:40
5
This post received KUDOS
2
This post was BOOKMARKED
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^2pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2pw2k=0 (E) 2w^2pw+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.



Manager
Joined: 07 Mar 2005
Posts: 93

i think choosing own rectangle = easiest and safest



Intern
Joined: 26 Sep 2012
Posts: 15

Re: ps CIRCUIT BOARD [#permalink]
Show Tags
25 Jul 2013, 02:18
1
This post was BOOKMARKED
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^2pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2pw2k=0 (E) 2w^2pw+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: 43853

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
25 Jul 2013, 02:24



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
25 Jul 2013, 02:29
3
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
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. Answer: E. Note that for plugin 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 Jul 2013
Posts: 2

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
25 Jul 2013, 03:47
In order to solve this problem algebraicaly we need the following formulaes:
\(Perimeter = 2*w + 2*h\) \(Area = w * h\)
We begin by observing what information we have. The lefthand side in both of the above formulae is known, and defined as p and k. We also have the width, w. We can then use what we know to find the height, by rearranging terms:
\(p= 2*w + 2*h\) ===> \(h = \frac{p2*w}{2}\).
Slot this into the formulae for the area to obtain
\(k= w * \frac{p2*w}{2}\) =====> \(2w^2  pw + 2k = 0\)



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
25 Jul 2013, 20:10
For a rectangle, if one side = w & perimeter = p, then the other side is (p2w)/2 So, area k = w x (p2w)/2 Solving the above, we get answer = E (2w^2  pw + 2k = 0)
_________________
Kindly press "+1 Kudos" to appreciate



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
19 Nov 2013, 06:24
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 Smart numbers here guys w = 2 l = 3 So P = 10 A = 6 Start by E always on these types of questions. E is the correct answer choice. And also try to use different numbers just in case. Here we used different numbers for length and width Needless to say try to avoid 0,1, or any negative numbers Cheers J



Intern
Joined: 21 Aug 2013
Posts: 8

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
16 May 2014, 02:35
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 I supposed the rectangle to be a square and w = 1 , then P = 4 and k = 1 (A) & (C) always positive so we can safely eliminate those choices and a quick calculation allows to eliminate (B) and (D) hence the correct answer is (E)



Director
Joined: 07 Dec 2014
Posts: 906

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
16 Feb 2016, 12:50
let k/w=rectangle length let p/2w=rectangle length k/w=p/2w 2w^2pw+2k=0



Moderator
Joined: 21 Jun 2014
Posts: 983
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
09 Apr 2016, 09:24
1
This post received KUDOS
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  720740 http://gmatclub.com/forum/informationonnewgmatesrreportbeta221111.html http://gmatclub.com/forum/listofoneyearfulltimembaprograms222103.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7946
Location: Pune, India

Re: A rectangular circuit board is designed to have width w inch [#permalink]
Show Tags
28 Nov 2017, 04:56
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 Answer (E)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)

Re: A rectangular circuit board is designed to have width w inch [#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 Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: A rectangular circuit board is designed to have width w inch
[#permalink]
29 Nov 2017, 17:13






