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Two More Tricky Problems for me

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Two More Tricky Problems for me

by rfshocker2255 » Sun Feb 10, 2013 10:44 am
A 40m long wire is cut into 2pcs. One forms a circle with radius r, and the other piece forms a square. What is the total area of the circle and square?

AND

For all positive integers, [m]=m/2 for all even integers and [m]=3m for all odd integers. What does [9] x [6] equal?
I keep coming up with 81, and am having a hard time understanding what I am missing.

Thanks for the help!!
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by Brent@GMATPrepNow » Sun Feb 10, 2013 10:58 am
rfshocker2255 wrote:A 40m long wire is cut into 2pcs. One forms a circle with radius r, and the other piece forms a square. What is the total area of the circle and square?
Here's the original question in its entirety:
A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

a) (pi)r^2
b) (pi)r^2 + 10
c) (pi)r^2 + (1/4)(pi)^2(r)^2
d) (pi)r^2 + [40 - 2(pi)r]^2
e) (pi)r^2 + [1O - (1/2)(pi)r]^2

Here's the algebraic approach:

Since r is the radius of the circle, the area of the circle will be (pi)r^2.

If r is the radius of the circle, the length of wire used for this circle will equal its circumference which is 2(pi)r

So, the length of wire to be used for the square must equal 40 - 2(pi)r

In other words, the perimeter of the square will be 40 - 2(pi)r

Since squares have 4 equal sides, the length of each side of the square will be [40 - 2(pi)r]/4, which simplifies to be 10 - (pi)r/2

If each side of the square has length 10 - (pi)r/2, the area of the square will be [10 - (pi)r/2]^2

So, the total area will equal (pi)r^2 + [10 - (pi)r/2]^2, which is the same as E

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Feb 10, 2013 11:09 am
rfshocker2255 wrote: For all positive integers, [m]=m/2 for all even integers and [m]=3m for all odd integers. What does [9] x [6] equal?
I keep coming up with 81, and am having a hard time understanding what I am missing.
You are correct in that [9] x [6] = 81

9 is odd, so [9] = (3)(9) = 27
6 is even, so [6] = 6/2 = 3
So, [9] x [6] = 27 x 3 = 81

However, the answer choices are as follows:

a) [81]
b) [54]
c) [37]
d) [27]
e) [18]

So, which of these equals 81?

Since 27 is odd, [27] = (3)(27) = 81

So, the correct answer is D

Cheers,
Brent
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by Anurag@Gurome » Sun Feb 10, 2013 10:00 pm
Refer to the posts as follows...

For problem 1 >> https://www.beatthegmat.com/geometry-t131113.html#516326
For problem 2 >> https://www.beatthegmat.com/function-pro ... tml#327643
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by hemant_rajput » Mon Feb 11, 2013 8:05 am
rfshocker2255 wrote:A 40m long wire is cut into 2pcs. One forms a circle with radius r, and the other piece forms a square. What is the total area of the circle and square?

AND

For all positive integers, [m]=m/2 for all even integers and [m]=3m for all odd integers. What does [9] x [6] equal?
I keep coming up with 81, and am having a hard time understanding what I am missing.

Thanks for the help!!
please post the full question to make it feasible for all the member to answer it.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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