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

Question

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.

adishail · Accepted Answer

v* = v - v/3

For sake of understanding, let v* = B

B = v - v/3

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

Or, (v*)* =   -  /3

8 = 2v/3 - 2v/9
v = 18

Bunuel · Answer

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.

niheil · Answer

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

Bunuel · Answer

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 .

niheil · Answer

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

mmcooley33 · Answer

(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  -  /3

tfincham86 · Answer

Thanks for the explanation.

OCDianaOC · Answer

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

Henry S. Hudson Jr. · Answer

v-\frac{v}{3}-( /3) 
after multiplying everything by 3 we obtain  3v-v-v+\frac{v}{3}=24

4v/3=24

v=18

flowertown · Answer

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

Probus · Answer

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

ScottTargetTestPrep · Answer

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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