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If 1/a^2 + a^2 represents the diameter of circle O and 1/a +

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somethingbetter
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If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink] New post   Updated on: 21 Oct 2013, 09:19
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If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12
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B

Originally posted by somethingbetter on 14 Sep 2007, 11:33.
Last edited by Bunuel on 21 Oct 2013, 09:19, edited 3 times in total.
Renamed the topic and edited the question.
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b14kumar
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Re: looks pretty simple , huh!! [#permalink] New post   14 Sep 2007, 11:58
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somethingbetter wrote:
If (1/a^2)+a^2 represents the diameter of circle O and (1/a)+a =3 , which of the following best approximates the circumference of circle O?

a. 28
b. 22
c. 20
d. 16
e. 12


Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh
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Re: looks pretty simple , huh!! [#permalink] New post   21 Oct 2013, 09:22
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AccipiterQ wrote:
b14kumar wrote:
somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12


Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh



Hi,

bumping an old question, but why would you square both sides of the equation...I see that it works, but I don't understand how one would know to do that.


We need to find the value of 1/a^2 + a^2, which is a second degree equation. 1/a + a = 3 is a first degree equation. Squaring seems very natural thing to do.
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[#permalink] New post   14 Sep 2007, 12:15
I get 22

(1/a + a) =3

(1/a + a) (1/a +a)=1/a^2 +a^2 +2

9-2=7

7*pi=22
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Re: looks pretty simple , huh!! [#permalink] New post   21 Oct 2013, 07:42
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b14kumar wrote:
somethingbetter wrote:
If (1/a^2)+a^2 represents the diameter of circle O and (1/a)+a =3 , which of the following best approximates the circumference of circle O?

a. 28
b. 22
c. 20
d. 16
e. 12


Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh



Hi,

bumping an old question, but why would you square both sides of the equation...I see that it works, but I don't understand how one would know to do that.
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink] New post   12 Apr 2016, 09:25
somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12


circumference = 2*pi*r
we are given that 1/a^2 + a^2 is diameter.

1/a + a = 3 -- take square

1/a^2 + a^2 = 7

hence r = 7/2

circumference = 22
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If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink] New post   30 Jan 2017, 04:16
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somethingbetter wrote:
If \(\frac{1}{a^2} + a^2\) represents the diameter of circle O and \(\frac{1}{a} + a = 3\), which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12


\(Circumference = 2πr\)

\(( \frac{1}{a} + a )( \frac{1}{a}+ a ) = \frac{1}{a^2} + 1 + 1 + a^2\)

\((3)(3) = \frac{1}{a^2}+ a^2 + 2\)

\(\frac{1}{a^2} + a^2 = 7 = Diameter\)

\(Circumference = 2πr = 2π ( \frac{7}{2} ) = 7π = 21.99 ≈ 22\)
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink] New post   21 Feb 2018, 14:15
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somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12


Squaring 1/a + a = 3, we have:

(1/a + a)^2 = 3^2

1/a^2 + a^2 + 2 = 9

1/a^2 + a^2 = 7

Since 1/a^2 + a^2 = 7 represents the diameter, the circumference is

7π ≈ 22

Answer: B
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink] New post   19 Oct 2022, 06:35
Hi! I understand all of it except for where did you get the " + 2" from after squaring the first equation?! I'm confused. Thanks so much.

b14kumar wrote:
somethingbetter wrote:
If (1/a^2)+a^2 represents the diameter of circle O and (1/a)+a =3 , which of the following best approximates the circumference of circle O?

a. 28
b. 22
c. 20
d. 16
e. 12


Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh
GMAT Club Bot
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + [#permalink]
19 Oct 2022, 06:35
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