The smaller rectangle in the figure above represents the original size

Question

https://gmatclub.com/forum/download/file.php?id=28105 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 2015-10-16_0901.png

EMPOWERgmatRichC · Accepted Answer

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

Mo2men · Answer

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

BrainLab · Answer

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.

camlan1990 · Answer

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

Ans: B

TheKingInTheNorth · Answer

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.

Show Spoiler

Attachment:

2015-10-16_0901.png

(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 .

GMATinsight · Answer

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

Video solution by  GMATinsight

https://www.youtube.com/watch?v=Ffkxiq0XOD8

Nylal · Answer

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?

JJSHHShank · Answer

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

JeffTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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

itsarudolf · Answer

Hey guys,

can you please, tell me how you got from this step:
w^2 + 250w – 15,000 = 0

to this final one:
(w + 300)(w – 50) = 0

?

I just cannot figure out how you factorised and ended up there.

Cheers

Bunuel · Answer

Check the links below:

Factoring Quadratics 
 Solving Quadratic Equations

7. Algebra 
     Theory   
 Math : Algebra 101 
 Algebra: Tips and hints 
 FOIL on the GMAT: Simplifying and Expanding 
 Factoring Quadratics 
 Solving Quadratic Equations  
 Using Algebra vs. Logic on GMAT Quant Questions 
     Questions   
 Tough Algebra Set 
 Algebra Ability Quiz by e-GMAT 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

IloveMBA123 · Answer

still don't get it, the question clearly specified the area of enlarged. How could the area of enlarged include the original too? otherwise what is the purpose of mentioning the area of enlarged?

EMPOWERgmatRichC · Answer

Hi waihoe520,

The prompt specifically refers to "the larger RECTANGULAR lot shown"... so the larger lot must be a rectangle. There are only two rectangles in the picture: the original lot with dimensions of 100 x 150 and the larger (rectangular) lot with dimensions of (100 + W) x (150 + W).
 
GMAT assassins aren't born, they're made,
Rich

gurudabl · Answer

Hi experts,
 Bunuel   EMPOWERgmatRichC   GMATinsight   JeffTargetTestPrep

w^2 + 250 w - 15000 = 0

It's hard to determine the value of w by doing a straight forward factorization. Therefore, can we use a reverse approach?
p * -q = -15,000 and p - q = 250 
(w+p) (w-q) 
w = -p and w = q --> This positive root is already given to us in the answer option. Therefore, the other root will be p * -50 = -15, 000 which will give us p = 300
300 -50 = 250 Satisfies the other equation as well. 
Therefore, the answer is 50. 
Please confirm.

Thank you.

EMPOWERgmatRichC · Answer

Hi gurudabl,

Your approach to this question works fine. I would not go so far as to say that it's necessarily a 'faster' approach though. Factoring the 15,000 might seem a little 'scary' at first, but we have a LOT of clues to work with:

1) We know that we're dealing with integers - and the answers are fairly 'nice' numbers to work with, so the solution will probably be a nice, round number. 
2) From the Quadratic, we know that we'll have one positive and one negative number - and the SUM will be +250. 
3) With the "15" in 15,000 we're probably going to have either 1x15 or 3x5, and then it's just a matter of distributing the three "0"s.

Since the sum is +250, it would make sense to place two of the "0s" with a 3...... so we have +300 - and with the remaining 'pieces' (the 5 and the third "0") we have 50....

+300 and -50 is +250, which is an exact match for what's in the equation (and which gives us the two roots).
 
GMAT assassins aren't born, they're made,
Rich

gurudabl · Answer

Hi  EMPOWERgmatRichC ,

Thank you for replying to my post. 
Yes, I agree my method will take longer as compared to factorizing this method with just intuition. I guess not having a Quant background does bite back.

You said, "1) We know that we're dealing with integers - and the answers are fairly 'nice' numbers to work with, so the solution will probably be a nice, round number". 
My question is how can you be so sure? 
Integer + Integer = Integer
Integer - Integer = Integer
Integer * Integer = Integer 
However, Integer/ Integer = (might / might not) be an Integer.
Is it because we have the product -15,000 and all the answer options are a factor of -15,000? 
I would like to know what is your thinking approach?

EMPOWERgmatRichC · Answer

Hi gurudabl,

While you are correct that dividing an integer by integer will often lead to a non-integer, that is NOT the case here. We're told that the larger rectangular area is TWICE the smaller rectangular area. We also know the dimensions of the smaller area (100 x 150) so we also know that it's an integer. Doubling an integer will give us another integer.

Looking at the drawing, we know that the larger dimensions are (100+W) and (150+W). The 5 answers are all integers, so both of those dimensions MUST also be integers. The moment you realize that the larger rectangle has an area of 30,000 you could immediately 'brute force' the possible dimensions of the larger rectangle if you wanted to (and once you find a value of W that gives us an overall area of 30,000 then you can stop working)....

Answer A: Is (100+25)(150+25) equal to 30,000. I bet you can tell me why NOT without actually doing that calculation (hint: rounding the second parentheses UP to the nearest "100" proves that that original product is too small AND should get you thinking about what the correct answer would be).

GMAT assassins aren't born, they're made,
Rich

gurudabl · Answer

Hi  EMPOWERgmatRichC

Thank you for your quick reply.
Yes, I think I'm getting a feel of it now. 
Since all the answer options are integers w has to be an integer and, therefore, both (100 + w) and (150 + w) have to be an integer which will equal to 30,000, an integer.

Regarding your question about option A. 
If I round second parentheses up to nearest "100" then it becomes 200 correct? 
(150 + 25) = 175 = 200
125 * 200 = 25,000 
Since the product of the two new dimensions has to equal 30,000 I assume I should start thinking of going to the next great value?

I wouldn't go up from option C. 75 since it has a unit digit 5 and if I look closely it will give me a unit of 5 in the final product.

Thank you.

The smaller rectangle in the figure above represents the original size

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The smaller rectangle in the figure above represents the original size

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