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# The smaller rectangle in the figure above represents the original size

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
The smaller rectangle in the figure above represents the original size [#permalink]

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15 Oct 2015, 22:03
3
17
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:34) correct 20% (02:20) wrong based on 1147 sessions

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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:

2015-10-16_0901.png [ 6.68 KiB | Viewed 14868 times ]

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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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15 Oct 2015, 23:34
2
2
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:
2015-10-16_0901.png

Area of the small rectangle: 150*100=15000
Area of the big one: 30000

(100+w)*(150+w)=30000 -> $$15000+100w+150w+w^2=30000 --> w^2+250w-15000=0$$
w=-300,50 Answer (B) it cannot be negative.
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The smaller rectangle in the figure above represents the original size [#permalink]

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Updated on: 16 Oct 2015, 01:43
6
2
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:
2015-10-16_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.

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.
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Posts: 110
Re: The smaller rectangle in the figure above represents the original size [#permalink]

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16 Oct 2015, 01:40
1
1
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:
2015-10-16_0901.png

(100+w)(150+w) = 2*100*150
=> (w-50)(w+300)=0
=> w=50

Ans: B
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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16 Oct 2015, 02:58
1
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:
2015-10-16_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+250w-15000=0

Solutions of this equation are w=-300 and 50.

As dimension can't be negative, value of w is 50. Option B

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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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16 Oct 2015, 18:45
1
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 +250w-100*150=0; solving this quadratic equation we get w = 50 or negative value. As negative value is not possible.

Thanks,
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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16 Oct 2015, 21:09
1
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 .
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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17 Oct 2015, 08:01
3
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:
2015-10-16_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 non-zero) 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

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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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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+250w-15000=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?
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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17 Oct 2015, 17:44
5
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.

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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 Schools: ISB '18, SPJ GMBA '17 GMAT 1: 680 Q48 V35 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: 2015-10-16_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 non-zero) 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+250w-15000=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(b2-4ac)]/2 in this case the equation is: w2+250w-150*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 1 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 Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11801 Location: United States (CA) GMAT 1: 800 Q51 V49 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 1 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 Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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20 Jun 2017, 23:12
imo b
(100+w) X (150+w) = 15000 x 2
w^2+250w-15000=0
w=50,-300
so w=50
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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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...
Is there something wrong with the english understanding i have, or its just that i hv to start understanding it that way??
Thanks
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Re: The smaller rectangle in the figure above represents the original size [#permalink]

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26 Jun 2017, 07:47
30000 = (100+w)*(150+w)

only option B satisfies this equation.

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The smaller rectangle in the figure above represents the original size [#permalink]

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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:
2015-10-16_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

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