Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46167

The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
15 Oct 2015, 22:03
Question Stats:
80% (02:34) correct 20% (02:20) wrong based on 1147 sessions
HideShow timer Statistics



Director
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
15 Oct 2015, 23:34
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png Area of the small rectangle: 150*100=15000 Area of the big one: 30000 (100+w)*(150+w)=30000 > \(15000+100w+150w+w^2=30000 > w^2+250w15000=0\) w=300,50 Answer (B) it cannot be negative.
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



SVP
Joined: 26 Mar 2013
Posts: 1674

The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
Updated on: 16 Oct 2015, 01:43
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png Area of big Rec= 2*Area of smaller rec=30000 (100+w)(150+w)=30000. By scanning and Testing the answers, so 50 will fit. Answer B
Originally posted by Mo2men on 16 Oct 2015, 01:35.
Last edited by Mo2men on 16 Oct 2015, 01:43, edited 2 times in total.



Manager
Joined: 11 Sep 2013
Posts: 110

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
16 Oct 2015, 01:40
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png (100+w)(150+w) = 2*100*150 => (w50)(w+300)=0 => w=50 Ans: B



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1045
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
16 Oct 2015, 02:58
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png My Solution:
Area of smaller rectangle : 100 x 150 = 15000 sqft
Area of larger rectangle : (100+w) X (150+w) = 15000 x 2 (Given,Twice the area of smaller rectangle)
Solving this, w^2+250w15000=0
Solutions of this equation are w=300 and 50.
As dimension can't be negative, value of w is 50. Option B
_________________
"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."



Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
16 Oct 2015, 18:45
We can write from given equation that area of bigger one is twice the smaller one; so (100+w)(150+w) = 2*100*150 there fore solving above equation we get: w^2 +250w100*150=0; solving this quadratic equation we get w = 50 or negative value. As negative value is not possible. Hence answer is 50; B
Thanks,



Manager
Joined: 13 Mar 2013
Posts: 173
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
16 Oct 2015, 21:09
The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Area of smaller rectangle = 100 * 150 = 15000 Area of larger = 2 * smaller = 30,000 Now given that both the length were increased by w . Hence new length =(100 + W ) and (150 + w) Area => 30,000 = (100 + W ) and (150 + w) Now use the option to check the value . substitute on the place of W . Option B perfectly fits the bill . hence the answer is B . Always try to use number and option . It is faster and easy than solving equation .
_________________
Regards ,



SVP
Joined: 08 Jul 2010
Posts: 2114
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
17 Oct 2015, 08:01
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png Area of original Plot = 100*150 Area of Enlarged Plot = (100+w)*(150+w) Given (100+w)*(150+w) = 2*(100*150) i.e. (100+w)*(150+w) = 30000 Checking Options: (A) 25 i.e. (100+w)*(150+w) = (100+25)*(150+25) (unit digit nonzero) is NOT equal to 30000 hence INCORRECT (B) 50 i.e. (100+w)*(150+w) = (100+50)*(150+50) = 150*200 = 30,000 hence CORRECT(C) 75 (D) 100 (E) 200 Answer: Option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 15 Sep 2015
Posts: 1

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
17 Oct 2015, 13:54
One question (not to the problem itself):
Is there any "shortcut" to find the solutions of the quation 15000+100w+150w+w^2=30000 > w^2+250w15000=0? Easy problem in general but took me (in total) almost 2min to find numbers that sum up to 250 and multiply to 15000?
Maybe I'm missing one of the "basic" concepts?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11801
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
17 Oct 2015, 17:44
Hi Nylal, The 'shortcut' that you're looking for is to actually AVOID doing the Quadratic altogether and instead TEST THE ANSWERS. Since you know that you're looking for a total area that equals 30,000, and you have 5 answers that are numbers, you just have to do enough basic multiplication to find the one answer that gives you that exact area. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 03 Aug 2015
Posts: 57
Concentration: Strategy, Technology

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
13 Feb 2016, 20:50
GMATinsight wrote: Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png Area of original Plot = 100*150 Area of Enlarged Plot = (100+w)*(150+w) Given (100+w)*(150+w) = 2*(100*150) i.e. (100+w)*(150+w) = 30000 Checking Options: (A) 25 i.e. (100+w)*(150+w) = (100+25)*(150+25) (unit digit nonzero) is NOT equal to 30000 hence INCORRECT (B) 50 i.e. (100+w)*(150+w) = (100+50)*(150+50) = 150*200 = 30,000 hence CORRECT(C) 75 (D) 100 (E) 200 Answer: Option B This looks to be a very good approach when compared to traditional Methods.... Thanks for your solution....



Intern
Joined: 07 Dec 2016
Posts: 11

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
07 Feb 2017, 14:24
Nylal wrote: One question (not to the problem itself):
Is there any "shortcut" to find the solutions of the quation 15000+100w+150w+w^2=30000 > w^2+250w15000=0? Easy problem in general but took me (in total) almost 2min to find numbers that sum up to 250 and multiply to 15000?
Maybe I'm missing one of the "basic" concepts? Hi Nylal how about : (150+W) * (100+W)= 2* 100*150 150*100+(100+150)w + W^2= 2*100*150 > 250w +w^2 = 2*100*150(150*100) > w(250+w) = 150*100 Now from the option we get Option B as 50 *300 or (50*3)*100 = 150*100.



Intern
Joined: 10 Mar 2013
Posts: 6

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
01 Jun 2017, 04:09
Solution for Quadratic equation: aX2 + bX+c=0 is, X=[b+Sqrt(b24ac)]/2 in this case the equation is: w2+250w150*100=0 hence, w=[250+sqrt(250*250+4*1*150*1000)]/2 or, w=[250+350]/2=50,300



Intern
Joined: 03 Jun 2017
Posts: 14

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
19 Jun 2017, 23:01
hi.. I have a kind of vauge understanding of the question. Correct me, where i am going wrong.. "If the area of the enlarged lot is twice the area of the original lot" Original is 15000. ENlarged lot is 30000. So the total area would be 45000... I know everyone cannot be wrong... help me understand the way all do... Thanks in advance



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
20 Jun 2017, 19:14
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 We are given a diagram, which represents a parking lot, with a smaller rectangle inside a larger rectangle. The dimensions of the smaller rectangle are 100 ft. by 150 ft., and the dimensions of the larger rectangle are (100 + w) ft. by (150 + w) ft. Since the area of the larger rectangle is twice that of the smaller rectangle, we can create the following equation: (w + 100)(w + 150) = 2(100 x 150) w^2 + 250w + 15,000 = 30,000 w^2 + 250w – 15,000 = 0 (w + 300)(w – 50) = 0 w = 300 or w = 50 Since w must be positive, w must be 50. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11801
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
20 Jun 2017, 19:15
Hi JJSHHShank, Based on the drawing, we can see that the original lot is INSIDE the enlarged lot, so it's not correct to call the total area 45,000 sq. ft. (since that would 'count' the area of the original lot twice). If you wanted to, you can use the two areas (enlarged lot = 30,000 sq. ft. and the original lot = 15,000 sq. ft.) to determine the area that is NOT a part of the original lot. That 'extra area' is 30,000  15,000 = 15,000 additional sq. ft. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1159
Location: India
Concentration: Operations, Marketing
GRE 1: 314 Q157 V157
GPA: 3.4
WE: Manufacturing and Production (Manufacturing)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
20 Jun 2017, 23:12
imo b (100+w) X (150+w) = 15000 x 2 w^2+250w15000=0 w=50,300 so w=50
_________________
Please give kudos if you found my answers useful



Intern
Joined: 03 Jun 2017
Posts: 14

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
23 Jun 2017, 08:58
Thanks Arvind, Empower and Jeff prep for the reply: From the discussion above, i understand that the enlarged lot includes the original lot too... So shudnt add it twice... Is there something wrong with the english understanding i have, or its just that i hv to start understanding it that way?? Thanks



Manager
Joined: 06 Jun 2013
Posts: 179
Location: India
Concentration: Finance, Economics
GPA: 3.6
WE: Engineering (Computer Software)

Re: The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
26 Jun 2017, 07:47
30000 = (100+w)*(150+w)
only option B satisfies this equation.
hence answer is B



Senior Manager
Joined: 20 Feb 2015
Posts: 386
Concentration: Strategy, General Management

The smaller rectangle in the figure above represents the original size [#permalink]
Show Tags
26 Jun 2017, 11:32
Bunuel wrote: The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w? (A) 25 (B) 50 (C) 75 (D) 100 (E) 200 Kudos for a correct solution.Attachment: 20151016_0901.png As given let area of the bigger rectangle be a then, a=2(150*100) a=30p where p=1000 can be solved in two ways. 1.substitute the values back , and we quickly come to know that it is B(150+50)*(100+50)=30p 2. 2(150*100)=(100+w)*(150+w) a bit lengthy , but it does give w=50 so B




The smaller rectangle in the figure above represents the original size
[#permalink]
26 Jun 2017, 11:32



Go to page
1 2
Next
[ 22 posts ]



