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The shaded portion of the rectangular lot shown above repres

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The shaded portion of the rectangular lot shown above repres [#permalink] New post 19 Dec 2012, 05:28
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Question Stats:

80% (02:33) correct 20% (02:22) wrong based on 475 sessions
Attachment:
Shaded region.png
Shaded region.png [ 17.6 KiB | Viewed 8608 times ]
The shaded portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) \(\sqrt{13}\)
(B) \(2\sqrt{13}\)
(C) 6
(D) 8
(E) 10
[Reveal] Spoiler: OA
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 19 Dec 2012, 05:34
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The shaded portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) \(\sqrt{13}\)
(B) \(2\sqrt{13}\)
(C) 6
(D) 8
(E) 10

Given that \(\frac{xy}{2}=24\) and \(x = y + 2\) --> \(xy=48\) --> \((y+2)y=48\).

\(z^2=x^2+y^2\) --> \(z^2=(y + 2)^2+y^2=2y^2+4y+4=2y(y+2)+4\).

Since \((y+2)y=48\), then \(z^2=2y(y+2)+4=2*48+4=100\) --> \(z=10\).

Answer: E.
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 17 Nov 2013, 19:25
What is the shaded part, the pentagon or the right angled triangle?
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 17 Nov 2013, 22:37
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 06 Mar 2014, 01:32
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 18 Nov 2014, 19:22
Walkabout wrote:
Attachment:
Shaded region.png
The shaded portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) \(\sqrt{13}\)
(B) \(2\sqrt{13}\)
(C) 6
(D) 8
(E) 10


I actually did this a different way.

For a triangle area=\(\frac{B*H}{2}\) so solving I get that \(B*H=48\) now I would solve by algebra, but the problem tells that the difference between x & y is two, so what two numbers multiply to 48 that separated by 2... 6 & 8. Since it doesn't matter which side is which length I saw this was a pythagorean triplet and z or the hypotenuse is 10.

Answer E

Just another way to think about this
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The shaded portion of the rectangular lot shown above repres [#permalink] New post 20 Nov 2014, 00:30
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Modified the diagram as shown below:

Attachment:
Shaded%20region.png
Shaded%20region.png [ 18.65 KiB | Viewed 2794 times ]


\(Area of shaded region = \frac{1}{2} x (x-2) = 24\)

\(x^2 - 2x - 48 = 0\)

x = 8

Base = 6; Height = 8

\(z = \sqrt{6^2+8^2} = \sqrt{100} = 10\)

Answer = E
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 11 Jan 2015, 04:03
Hi,

This one was tricky, not because the solution was difficult, but because of my mistakes in the calculations...

I also used Paresh's approach, but instead of solving for y and getting y=x-2, I just used y and y+2. But, I couldn't see the 6*4=48 ... so I couldn't find the possible solutions of the equation easily!

In fact I did this:
Area= (b*2) / 2
24=[y(y+z)] / 2
24= (y^2 + 2y) / 2
48 = y^2 + 2y
y^2 + 2y - 48 = 0.

I didn't see these solutions: -6, 8 and ended up using the quadratic formula, which is not handy when you are not quick with calculations! Haha! So, I passed the time...

Just as a small piece of advice, in similar situations, what makes it easier to find the roots is to make the prime factorization of the constant. Then you end up with this 2*2*2*2*3, so you have fewer values to test and find one that works.
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 21 Jun 2015, 14:52
Great OG problem. Paresh's solution helped me see the light on this one. The others made sense, but I may not see that relationship on test day. Re-labeling the figure with the formulas will help add clarity. Great explanation!
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 21 Jun 2015, 19:11
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Hi All,

On certain GMAT questions, you can "brute force" the work and quickly come up with the correct answer. Here's how:

From the prompt and the picture, we know that…
1) The triangle is a right triangle (because it's in the "corner" of a rectangle)
2) The two legs of the triangle differ by 2
3) The area of the triangle is 24 (A = (1/2)(B)(H))

Let's focus on the area = 24 for a moment. We know the two legs differ by 2, so we can probably "brute force" the possibilities and find the match:

If the legs are:
2 and 4, then the area = 4
4 and 6, then the area = 12
6 and 8, then the area = 24 ---> that's THE match

If the legs are 6 and 8, then we can use the Pythagorean Formula to figure out the value of Z. You might also recognize the "Pythagorean Triplet" and solve the problem that way.

Final Answer:
[Reveal] Spoiler:
E


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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 01 Jul 2015, 04:49
I liked your approach, Simple and time saving, however not applicable in all cases.
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Re: The shaded portion of the rectangular lot shown above repres [#permalink] New post 01 Jul 2015, 18:14
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Hi jaspreets,

As you continue to study for the GMAT, you're going to find that 'shortcuts' vary from question to question, but there are almost always shortcuts to found (and in many cases there are alternative ways to approach the question besides 'just doing the math'). It's to your benefit to learn to spot the 'clues' that hint at these options - and then practice using those approaches. While not every shortcut will be available on every question, the list of possible shortcuts is definable, so you can train to use them again and again on Test Day.

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Re: The shaded portion of the rectangular lot shown above repres   [#permalink] 01 Jul 2015, 18:14
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