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505-555 (Easy)|   Geometry|                           
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GMATinsight
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The smaller rectangle in the figure above represents the original size 07 Jun 2020, 22:05
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gurudabl
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.
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Quote:

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
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gurudabl This is how I did this problem. :)

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
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The smaller rectangle in the figure above represents the original size 08 Jun 2020, 15:02
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gurudabl
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.
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Hi gurudabl,

YES - that is correct. As you continue to study, you should take advantage of ALL of the information that the prompt gives you to work with (and that includes the 5 answer choices). In many cases, the 'format' of the answers will provide a clue that will help you to take advantage of faster approaches to getting to the correct answer.

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The smaller rectangle in the figure above represents the original size 22 Jun 2021, 23:09
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Hey guys,
I had an interesting method that I figured out while analysing the question which I wished I had done while solving.
Mathematically, this boils down to the following equation:

100*150*2=(100+w)(150+w)

Now this 2 can be multiplied to either 100 or 150 and the only cases for LHS are:
A) 200*150
Or
B) 100*300
Now case B is rejected because w is being added to both 100 and 150 and it can't be 0 for one and 150 for another!
So the only case left is 200*150
This implies that 50 was added to both the length and breadth

Thus B is our ans.
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The smaller rectangle in the figure above represents the original size 09 Oct 2021, 20:06
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Can someone please explain for me why we don't subtract the smaller rectangle when calculating the enlarged lot area?

Thank you.
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The smaller rectangle in the figure above represents the original size 09 Oct 2021, 22:42
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Bunuel

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



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Attachment:
2015-10-16_0901.png
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Original area was \(100*150 = 15000\)

Increased Area is \((100 + w)(150 + w) = 30000\)

Check the options \(30000 = 150 * 200\), hence Answer must be (B)
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The smaller rectangle in the figure above represents the original size 10 Oct 2021, 19:12
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dungltp9
Can someone please explain for me why we don't subtract the smaller rectangle when calculating the enlarged lot area?

Thank you.
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Hi dungltp9,

The prompt refers specifically to the "larger RECTANGULAR lot shown." If you remove the smaller rectangle from your calculation, then what's left would NOT be a rectangle.

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The smaller rectangle in the figure above represents the original size 10 Nov 2021, 03:18
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From the given information it follows that
(100 + w)(150 + w) = 2(100)(150), or
(100 + w)(150 + w) = (200)(150). This is a
quadratic equation that can be solved by several
methods. One method is by inspection. The left
side is clearly equal to the right side when w =50.
Another method is by factoring. Expanding the left
side gives (100)(150) + 250w + v} =(200)(150), or
v} + 250w - (100)(150) = 0. Factoring the left
side gives ( w - 50)( w + 300) = 0, which has
w =50 as its only positive solution.
The correct answer is B
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The smaller rectangle in the figure above represents the original size 09 Jul 2022, 01:05
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2 x 100 x 150 = (100 + w) x (150 + w)
200 x 150 = (100 + w) x (150 + w)

Put w = 50, and voila solved:
200 x 150 = (100 + 50) x (150 + 50)
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The smaller rectangle in the figure above represents the original size 01 Feb 2023, 09:48
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Bunuel JeffTargetTestPrep I factorized the equation w^2 + 250w - 15000 = 0 into w^2 + 150w + 100w + 15000 = 0 instead of w^2 + 300w - 50w - 15000 = 0
and got w = -150 or 100. Where did I go wrong?
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The smaller rectangle in the figure above represents the original size 08 Feb 2023, 23:25
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Anubhav21
Bunuel JeffTargetTestPrep I factorized the equation w^2 + 250w - 15000 = 0 into w^2 + 150w + 100w + 15000 = 0 instead of w^2 + 300w - 50w - 15000 = 0
and got w = -150 or 100. Where did I go wrong?
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Hello Anubhav21,

I see you are not comfortable with solving quadratic equations. So, let me first explain the general way of splitting the X-coefficient to solve quadratic equations and then we shall solve this question.

“SPLITTING THE X-coefficient METHOD” TO SOLVE QUADRATIC EQUATION

The steps to solve a quadratic equation under this method involve:

  • Write the quadratic equation in the standard form, ax\(^2\) + bx + c = 0.
  • Identify the values of a, b and c.
    1. Example: In 2x\(^2\) + 5x + 2 = 0, a = 2, b = 5 and c = 2.
    2. Example: 2x\(^2\) -5x + 2 = 0. Here, a = 2, b = -5 and c = 2.
  • To simplify the quadratic equation, the coefficient of x (b) must be split into two terms b\(_1\) and b\(_2\), such that:
    1. b\(_1\) + b\(_2\) = b and
    2. b\(_1\)b\(_2\) = ac.
  • Now, the equation will have changed to ax\(^2\) + b\(_1\)x + b\(_2\)x + c = 0. Finally, we take “pair-wise common factors out” to get a completely factored form of the quadratic equation. (Read the explanation below on your equation to best understand this)

APPLYING THIS METHOD ON THE QUESTION IN HAND

In the solution to this question, we arrived at the quadratic equation: w\(^2\) + 250w – 15000 = 0.

Let me first discuss what you did incorrectly and then show the correct simplification.

  • You wrote w\(^2\) + 250w – 15000 as w\(^2\) + 150w + 100w – 15000.
    • So, you took b\(_1\) = 150 and b\(_2\) = 100.
    • Now, although the sum of 150 and 100 correctly gives us 250 (= b), their product does NOT give -15000 (= ac) as required.
  • You most likely missed the sign that the constant term came with.
    • In this equation, a = 1 and c = - 15000. Hence, product of a and c (ac) = -15000
  • To do this correctly, b (=250) had to be split such that product of b\(_1\) and b\(_2\) would be -15000 and not 15000.
    • Another try should give you that b can be split into 300 and -50.

Hence, correct split of equation w\(^2\) + 250w – 15000 = 0 is w\(^2\) + 300w -250w – 15000 = 0.

Now, continue solving the question. Reach back to us if you still have any doubt. 😊


Hope this helps!

Best Regards,
Ashish Arora
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The smaller rectangle in the figure above represents the original size 12 Sep 2024, 08:45
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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?


\(100 * 150 = 15,000\)

\(15,000 * 2 = 30,000\)

\((w+100)(w+150) = 30,000\)

\(w^{2}+250w+15,000 = 30,000\)

\(w^{2}+250w-15,000 = 0\)

\((w+300)(w-50) = 0\)

\(w=-300\)

\(w=50\)

Answer B
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The smaller rectangle in the figure above represents the original size 20 Feb 2026, 02:10
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