A third Problem Solving question

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A third Problem Solving question [#permalink]

06 Oct 2010, 12:26

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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.

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Re: A third Problem Solving question [#permalink]

06 Oct 2010, 12:42

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niheil wrote:

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: A third Problem Solving question [#permalink]

06 Oct 2010, 12:52

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niheil wrote:

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: A third Problem Solving question [#permalink]

06 Oct 2010, 13:06

Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?

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Re: A third Problem Solving question [#permalink]

06 Oct 2010, 13:14

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: A third Problem Solving question [#permalink]

06 Oct 2010, 13:22

Awesome! I understand. Thanks Bunuel! And thanks again adishail!

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new [#permalink]

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: new [#permalink]

11 Dec 2010, 09:52

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Merging similar topics. Refer to the solutions above. Please ask if anything remains unclear.
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Re: A third Problem Solving question [#permalink]

13 Dec 2010, 08:42

Thanks for the explanation.
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Re: A third Problem Solving question [#permalink] 13 Dec 2010, 08:42

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A third Problem Solving question

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