Gprep Pack 1 - Circle

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Gprep Pack 1 - Circle

by greenwich » Mon Oct 15, 2012 3:07 pm

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What is the circumference of circular region R?

(1) The area of R is 36 pi.
(2) The area of a square region inscribed in R is 72.
Source: — Data Sufficiency |

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by vikram4689 » Mon Oct 15, 2012 9:31 pm

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before i begin the solution, a very useful,general tip for DS ; ALWAYS write simplified DS question with constraints.

you need to find circumference=2*pi*R or i can say you need "R"

i) Area=pi*R*R=36pi...... so you can find R (suff.)
ii) Area of square region in circle=72
diagonal of square will be diameter because angle drawn from 2 end-points of a diameter make 90 degrees angle on the circle. since diagonalof square=2R.. you can find side of square and hence area of square in terms of R. That means you can find R.(suff.)

Ans = D
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by greenwich » Tue Oct 16, 2012 7:33 am

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In (1), R^2=36, R could be 6 or -6. Why -6 is not being considered in this case?

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by anuprajan5 » Tue Oct 16, 2012 9:46 am

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Hi,

When you have a square, then the square root of that is always positive on the GMAT.

for example, x^2, when square rooted is mod x which is always positive.

But if you have a number that is being square rooted, for example 9, then it has 2 options - positive 3 and negative 3.

Plus quite honestly, I understand the usage of the above principle for number theory but there is never going to a circle with a negative radius.

Regards
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by vikram4689 » Wed Oct 17, 2012 12:43 am

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anuprajan5 wrote: But if you have a number that is being square rooted, for example 9, then it has 2 options - positive 3 and negative 3.
Above statement is wrong as it implies sq.rt.(9) = +3, -3 BUT
sq.rt.(9) = +3 only
and, x^2=9 ==>> x = +3,-3


To greenwich ,Answer is your question is given correctly by anupranjan5 and is quoted below
there is never going to a circle with a negative radius.
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by alanforde800Maximus » Fri May 18, 2018 12:26 am

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Experts,

Can you please share your insights on this problem?