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

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niheil
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For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   06 Oct 2010, 12:26
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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

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My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.
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B
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adishail
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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   06 Oct 2010, 12:42
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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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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   06 Oct 2010, 12:52
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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: \(v=?\)

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

Answer: B.
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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   06 Oct 2010, 13:06
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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] New post   06 Oct 2010, 13:14
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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] New post   06 Oct 2010, 13:22
Awesome! I understand. Thanks Bunuel! And thanks again adishail!
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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   11 Dec 2010, 09:36
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] New post   13 Dec 2010, 08:42
Thanks for the explanation.
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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   10 Feb 2018, 14:54
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] New post   14 Feb 2018, 12:04
\(v-\frac{v}{3}-([v-\frac{v}{3}]/3)\)
after multiplying everything by 3 we obtain \(3v-v-v+\frac{v}{3}=24\)

\(4v/3=24\)

\(v=18\)
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Re: For all real numbers v, the operation is defined by the equation v* = [#permalink] New post   05 Sep 2018, 08:26
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] New post   23 Apr 2019, 18:06
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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] New post   13 Dec 2020, 05:34
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niheil wrote:
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

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


Solution:

We can let w = v*; thus, we have (v*)* = w* = 8. That is,

w - w/3 = 8

2w/3 = 8

w = 8 x 3/2 = 12

Now, we earlier defined w = v*, and since w = 12, we have w = v* = 12, or:

v - v/3 = 12

2v/3 = 12

v = 12 x 3/2 = 18

Answer: B
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Re: For all real numbers, the operation v* is defined by the [#permalink] New post   10 Jan 2024, 07:57
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