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Titleist
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Rectangle ABCD has a width of 2.25, and length CD is a Updated on: 19 Oct 2005, 07:35
Originally posted by Titleist on 18 Oct 2005, 15:03.
Last edited by Titleist on 19 Oct 2005, 07:35, edited 1 time in total.
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Rectangle ABCD has a width of 2.25, and length CD is a subset of values of the infinite set of values in equation Y=0. Rectangle ABCD also has three points in common with parabola Y=X^2-4X+1.75, which has exactly 2 points in common with equation Y=0. If the difference between the two common points of parabola Y=X^2-4X+1.75 and line Y=0 equals the range of values in common between rectangle side CD and line Y=0 then what is the area of rectangle ABCD?

A)6.25
B)6.75
C)7.0
D)7.25
E)9.0


You have 2 mins to solve! :boxer2



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gsr
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Rectangle ABCD has a width of 2.25, and length CD is a 18 Oct 2005, 15:31
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Is it B) 6.75

Took me 3 mins!
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mbaqst
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Rectangle ABCD has a width of 2.25, and length CD is a 18 Oct 2005, 16:24
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This Q is insane!!

j/k. A quick glance at the Q discouraged me from even setting up. Will try to get back soon.
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nero44
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Rectangle ABCD has a width of 2.25, and length CD is a 18 Oct 2005, 16:27
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3*2.25 = 6.75

took me a lot more than 2 or 3 minutes hahaha...
I had to plug in a lot of values before I had an idea of the parabola and what was acutally meant by the difference...


I hope these questions are not from an official gmat test... :S

actually the calculations are not much, but to grasp the essence of the stem takes a while... in testing conditions I would probably get nervous and freak out :P
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gsr
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Rectangle ABCD has a width of 2.25, and length CD is a 18 Oct 2005, 16:35
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a=?
b=2.25
a lies on line y=0 which is x axis.
parabola Y=X^2-4X+1.75 cuts y=0 at 2 points.
y=Y=X^2-4X+1.75 => Y=X^2-4X+1.75 = 0
solving for x, we get x=3.5 and 0.5
the wordy problem says that difference btw these two roots is a, which = 3
so area = ab = 3*2.25 = 6.75
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Rectangle ABCD has a width of 2.25, and length CD is a 18 Oct 2005, 17:36
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gsr
a=?
b=2.25
a lies on line y=0 which is x axis.
parabola Y=X^2-4X+1.75 cuts y=0 at 2 points.
y=Y=X^2-4X+1.75 => Y=X^2-4X+1.75 = 0
solving for x, we get x=3.5 and 0.5
the wordy problem says that difference btw these two roots is a, which = 3
so area = ab = 3*2.25 = 6.75
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sums it up nicely gsr!

here's another approach: Y=0 is obviously a fancy term for X-axis.

Draw the x and y axis.

The question stem tells you that the parabola has two X intercepts when it says that it has 2 points in common with Y=0.

To derive the two points quickly use the quadratic formula:

-b +/- Sqrt(b^2-4ac)/2a

you get 4+or-sqrt(-4^2-4(1)(7/4))/2(1) which gives both 0.5 and 3.5

3.5-0.5=3 which is the length of rectangle ABCD

3 x 2.25 = 6.75

refer to picture below
Attachments

parabola3.JPG
parabola3.JPG [ 12.46 KiB | Viewed 1170 times ]

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jdtomatito
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Rectangle ABCD has a width of 2.25, and length CD is a 19 Oct 2005, 01:07
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The stem is scary but the problem itself is very easy. Too much wording for a quite simple problem.
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Rectangle ABCD has a width of 2.25, and length CD is a 19 Oct 2005, 01:15
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Solving X^2 - 4x + 1.75 = 0 we get x to be either 3.5 or .5. The difference between them is 3. This is the length. We are already given the width as 2.25. So the answer is 2.25*3 = 6.75.

I took 2 mins to understand and figure out the problem, and a minute to work out and a minute to verify.
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Rectangle ABCD has a width of 2.25, and length CD is a 19 Oct 2005, 14:29
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krisrini
Solving X^2 - 4x + 1.75 = 0 we get x to be either 3.5 or .5. The difference between them is 3. This is the length. We are already given the width as 2.25. So the answer is 2.25*3 = 6.75.

I took 2 mins to understand and figure out the problem, and a minute to work out and a minute to verify.
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did you use the quadratic formula to find 3.5 and 0.5 as the x intercepts?
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Rectangle ABCD has a width of 2.25, and length CD is a 19 Oct 2005, 21:33
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Titleist
krisrini
Solving X^2 - 4x + 1.75 = 0 we get x to be either 3.5 or .5. The difference between them is 3. This is the length. We are already given the width as 2.25. So the answer is 2.25*3 = 6.75.

I took 2 mins to understand and figure out the problem, and a minute to work out and a minute to verify.

did you use the quadratic formula to find 3.5 and 0.5 as the x intercepts?
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Yes titleist, I used the quadriatic formula to get 3.5 and 0.5



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