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ABCD encloses a circle

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ABCD encloses a circle

by sanju09 » Thu Feb 09, 2012 4:39 am
Square ABCD encloses a circle of area 154 at its center. If π (pi) is taken to be 22/7 here, what area of the square ABCD is not circle?
I. The shortest distance from any of the four vertices A, B, C, or D of the square ABCD to the circle is 10√2 - 7.
II. The length of tangent drawn from any of the four vertices A, B, C, or D of the square ABCD to the circle is √151.





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Last edited by sanju09 on Mon Feb 13, 2012 2:42 am, edited 1 time in total.
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by Mike@Magoosh » Sun Feb 12, 2012 9:13 pm
Hello, Mr. Saxena,

I like the design of this question.

I will point out though, that it is not quite up to rigorous GMAT DS standards, because Statement #1 and Statement #2 are inconsistent with each other. Admittedly, many students will arrive at the correct answer of D without doing all the calculations and discovering this. Nevertheless, the DS of the real GMAT and of all respected GMAT question sources adhere to this standard.

I constructed a scaled diagram of the situation, based on the prompt and the information in Statement #1. That's the first diagram below (the lower one). Then, in a second diagram (the higher one), I added the tangent segment, and calculated its length, and the length was close to, but not equal to, the number you gave in Statement #2.

If I may make a suggestion -----
(a) in the prompt, make the area of the circle 49*pi
(b) in Statement #1, make the shortest distance equal to 34
(c) in Statement #2, make the tangent segment equal to 40

Then all statements are consistent, and the logic of the problem is unchanged.

Mike :)
Attachments
scaled diagram, statement #1.jpg
Scaled diagram, based on Statement #1
scaled diagram, with statement #2.jpg
Same scaled diagram, with Statement #2 info added
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by sanju09 » Mon Feb 13, 2012 2:47 am
Mike@Magoosh wrote:Hello, Mr. Saxena,

I like the design of this question.

I will point out though, that it is not quite up to rigorous GMAT DS standards, because Statement #1 and Statement #2 are inconsistent with each other. Admittedly, many students will arrive at the correct answer of D without doing all the calculations and discovering this. Nevertheless, the DS of the real GMAT and of all respected GMAT question sources adhere to this standard.

I constructed a scaled diagram of the situation, based on the prompt and the information in Statement #1. That's the first diagram below (the lower one). Then, in a second diagram (the higher one), I added the tangent segment, and calculated its length, and the length was close to, but not equal to, the number you gave in Statement #2.

If I may make a suggestion -----
(a) in the prompt, make the area of the circle 49*pi
(b) in Statement #1, make the shortest distance equal to 34
(c) in Statement #2, make the tangent segment equal to 40

Then all statements are consistent, and the logic of the problem is unchanged.

Mike :)
You are correct Mike@Magoosh. I have therefore made a very little change in the prompt, please see if it works.
Square ABCD encloses a circle of area 154 at its center. If π is taken to be 22/7 here, what area of the square ABCD is not circle?
I. The shortest distance from any of the four vertices A, B, C, or D of the square ABCD to the circle is 10√2 - 7.
II. The length of tangent drawn from any of the four vertices A, B, C, or D of the square ABCD to the circle is √151.
Thanks in either case.
The mind is everything. What you think you become. -Lord Buddha



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by Mike@Magoosh » Mon Feb 13, 2012 9:58 am
Hello, Mr. Saxena,

While the numbers now work out perfectly in this recent version, with all due respect, I can't tell you how much it rubs the mathematician in me the wrong way to use 22/7 for π. As you know, π is a remarkable number, irrational and transcendental, known to trillions of decimal places. It feels like a kind of mathematical sacrilege to reduce it to a rational number approximation. That's just my personal taste.

I do know that, while the GMAT expects approximations on problems with large numbers, I have no evidence that the GMAT would ever approximate, say, a mile as 5000 ft. In the problems where the GMAT expects the test-taker to approximate, the GMAT itself is still absolutely precise. Much in the same spirit, I believe approximating π as 22/7 is something the GMAT would not do, at least in the explicit information it was presenting in a problem. I have never known the mathematical information explicitly appearing on the GMAT to be anything less than rigorously correct in every respect.

The GMAC holds high standards, and we all strive to support our students in reaching these standards. If by my words, I can give you any support at all in producing questions that match those standards, then it is my honor and my pleasure.

With sincere respect,
Mike :)
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by sanju09 » Mon Feb 13, 2012 11:50 pm
Mathematician of certain countries approximate π to 22/7 not for irritating the mathematician of fellow countries, in fact they do so to ease the calculations involved and of course to pay some homage to the great thinker of his time, Archimedes. Anyways, I have no issues with the high standards the GMAC establishes and I am always there to learn more about it.

https://en.wikipedia.org/wiki/File:Domen ... s_1620.jpg

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