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

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For all real numbers, the operation v* is defined by the [#permalink] New post 10 Jan 2004, 12:30
For all real numbers, the operation v* is defined by the equation
v* = v-v/3. If (V*)* = 8, then v=

15
18
21
24
27

No idea how to tackle this problem. Any suggestion? :?:
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 [#permalink] New post 10 Jan 2004, 12:59
D) 24

(v-v/3)-v/3=8
v- 2v/3=8
3v-2v=24
v=24
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 [#permalink] New post 10 Jan 2004, 13:08
Could you explain how you came up to (v-v/3)-v/3=8 ???
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 [#permalink] New post 10 Jan 2004, 13:14
It is given in the question

v* = v - v/3
It follows that (v*)* = (v - v/3) - v/3
You have to perform the operation * twice.
The first part in parenthesis ( v - v/3 ) is for the first v*
Now, (v*)* is just (v - v/3) - v/3
Since it says that (v*)* = 8 then (v - v/3) - v/3 = 8
And then you just solve
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 [#permalink] New post 10 Jan 2004, 13:19
I am getting 18.

v* = v - v/3

So,

(v*)* is (v - v/3) - (v-v/3)/3 = 8

(2v/3)-(2v/9) = 8

4v/9 = 8

v=18
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 [#permalink] New post 10 Jan 2004, 13:32
Geethu, you're right! Still at work on a saturday doing this between clients :oops: :wall
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 [#permalink] New post 10 Jan 2004, 13:45
Very good! :P
Now I understood. First we modify v*, which will be (v-v/3)*, and then substitute v again!! That was a tricky one.
Thanks.

The answer is B.
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 [#permalink] New post 10 Jan 2004, 23:13
I got 18 too.. my way was to back solve. its easy too
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  [#permalink] 10 Jan 2004, 23:13
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For all real numbers, the operation v* is defined by the

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