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

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Manager
Joined: 05 Jul 2006
Posts: 197
For all real numbers v, the operation v* is defined by the [#permalink]

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12 Sep 2006, 11:56
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16. For all real numbers v, the operation v* is defined by the equation v* = v - v/3 . If (v*)* = 8, then v =

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
SVP
Joined: 05 Jul 2006
Posts: 1747

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12 Sep 2006, 12:04
My ANSWER IS B

fisrst simplify v-v/3 = 2/3v name it b thus v* = b

(v*)* = b* = 2/3b = 2/3(2/3v) = 4/9v

given that (v*)* = 8

thus 4/9v = 8 therfore v = 18
Senior Manager
Joined: 14 Jul 2005
Posts: 402

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13 Sep 2006, 23:22
Let x = v* = v-v/3,

Hence (v*)* = 8
x* = 8
x-x/3=8
i.e. 2x=24
x=12

i.e. v-v/3 = 12 => 2v=36 => v=18
Manager
Joined: 14 Sep 2006
Posts: 198
Schools: Olin Business School - Washington University

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14 Sep 2006, 01:58
B.

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

Plugged in numbers to solve more quickly:

(21-7) - (21-7)/3 = 8
14 - 14/3 =8
NO

(18-6) - (12)/3 = 8
12-4 = 8
YEP.
14 Sep 2006, 01:58
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# For all real numbers v, the operation v* is defined by the

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