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For all real numbers v, the operation is defined by the equation v* =

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Joined: 06 Oct 2010
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For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 11:26
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For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.
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Joined: 06 Jun 2009
Posts: 233
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 11:42
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niheil wrote:
Please explain how to solve the following question. It was listed in one of the GMAT Paper Tests.

16. For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.

v* = v - v/3

For sake of understanding, let v* = B

B = v - v/3

Therefore, (v*)* = B* = B-B/3

Or, (v*)* = [v- v/3] - [v- v/3]/3

8 = 2v/3 - 2v/9
v = 18
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Joined: 02 Sep 2009
Posts: 64951
Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 11:52
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niheil wrote:
Please explain how to solve the following question. It was listed in one of the GMAT Paper Tests.

16. For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.

Given: $$v*=v-\frac{v}{3}=\frac{2}{3}v$$ and $$(v*)*=8$$.
Question: $$v=?$$

$$(v*)*=(\frac{2}{3}v)*=\frac{2}{3}*(\frac{2}{3}v)=8$$ --> $$\frac{4}{9}v=8$$ --> $$v=18$$.

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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 12:06
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Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 12:14
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niheil wrote:
Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?

$$v*=v-\frac{v}{3}=\frac{2}{3}v$$ so $$v*$$ is $$\frac{2}{3}$$rd of $$v$$. So $$(\frac{2}{3}v)*$$ is $$\frac{2}{3}$$rd of $$\frac{2}{3}v$$.
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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06 Oct 2010, 12:22
Awesome! I understand. Thanks Bunuel! And thanks again adishail!
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Joined: 31 Oct 2010
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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11 Dec 2010, 08:36
ywilfred wrote:
For all real numbers v, the operation v* is defined by the equation v* = v - v/3 . If (v*)* = 8, what is the value of v.

Since v* = v - v/3,

(v*)* = (v - v/3) - (v - v/3)/3
= (3v-v)/3 - [(3v-v)/3]/3
= 2v/3 - (2v/3)/3
= 2v/3 - 2v/9
= (6v - 2v)/9
= 4v/9

We also know that (v*)* = 8, so (v*)* = 8 = 4v/9 and v = 18.

(v-v/3) did you just multiply by three to just make the v/3 go away? but then why does the first part get divided by three, its late here so the synapses arent firing at full speed scotty.

im losing the progression from (v-v/3) - (v-v/3)/3 --------> (3v-v)/3 - [(3v-v)/3]/3
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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13 Dec 2010, 07:42
Thanks for the explanation.
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Joined: 16 Oct 2017
Posts: 35
Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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10 Feb 2018, 13:54
Is this also a correct way to solve?

Step 1:
V* = V/1 - V/3
= 3V/3 - V/3 = 2V/3 = 8
2V = 24
V = 12

Step 2: 2V/3 = 12
2V/2 = 36/2
2V = 36
V = 18
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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14 Feb 2018, 11:04
$$v-\frac{v}{3}-([v-\frac{v}{3}]/3)$$
after multiplying everything by 3 we obtain $$3v-v-v+\frac{v}{3}=24$$

$$4v/3=24$$

$$v=18$$
Intern
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Posts: 2
Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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05 Sep 2018, 07:26
Bunuel wrote:
niheil wrote:
Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?

$$v*=v-\frac{v}{3}=\frac{2}{3}v$$ so $$v*$$ is $$\frac{2}{3}$$rd of $$v$$. So $$(\frac{2}{3}v)*$$ is $$\frac{2}{3}$$rd of $$\frac{2}{3}v$$.

Thanks for the explanation. But why (2/3V)* doesn't have a (2/3)* x V* but simply only give 2/3 x V*?
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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23 Apr 2019, 17:06
1
flowertown wrote:
Bunuel wrote:
niheil wrote:
Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?

$$v*=v-\frac{v}{3}=\frac{2}{3}v$$ so $$v*$$ is $$\frac{2}{3}$$rd of $$v$$. So $$(\frac{2}{3}v)*$$ is $$\frac{2}{3}$$rd of $$\frac{2}{3}v$$.

Thanks for the explanation. But why (2/3V)* doesn't have a (2/3)* x V* but simply only give 2/3 x V*?

Hi

V*= V-$$\frac{V}{3}$$
(V*) = $$\frac{2V}{3}$$

$$(V*)^{*}$$= $$\frac{2V}{3}$$ - $$\frac{\frac{2V}{3} }{3}$$
$$(V*)^{*}$$=$$\frac{2V}{3}$$-$$\frac{2V}{9}$$

We are told that $$(V*)^{*}$$= 8
hence
we solve for V = 18

Hope this helps
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Re: For all real numbers v, the operation is defined by the equation v* =  [#permalink]

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16 May 2020, 13:10
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Re: For all real numbers v, the operation is defined by the equation v* =   [#permalink] 16 May 2020, 13:10