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Math Expert V
Joined: 02 Sep 2009
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For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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Difficulty:   15% (low)

Question Stats: 76% (01:19) correct 24% (02:14) wrong based on 152 sessions

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Tough and Tricky questions: Functions.

For all real numbers V, the operation V* is defined by the equation V* =V − V/2 . If (V*)* = 3, then V =

A) 12
B) 6
C) 4
D) $$\sqrt{12}$$
E) −12

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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We know that V* = V-0.5V
Now (V*)* means we substitute the expression for V* into every instance of V:
(V-0.5V)-(V-0.5V)/2 = V-3/4V=1/4V = 3
So, V = 12.

Choice A
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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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V* is defined by the equation V* =V − V/2.... effectively we are halving the value of V.
In (V*)* function halving is done twice.
V*1/2*1/2=3
V=12

Ans = A
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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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$$V* = V − \frac{V}{2}$$

$$V* = V (1 - \frac{1}{2})$$

$$(V*)* = (V*) * \frac{1}{2}$$

$$3 = V * \frac{1}{2} * \frac{1}{2}$$

V = 3*2*2 = 12

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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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every V* is a half of correspondent V. We have two V*, final is 3, so 3*2=6 and 6*2=12

A
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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Functions.

For all real numbers V, the operation V* is defined by the equation V* =V − V/2 . If (V*)* = 3, then V =

A) 12
B) 6
C) 4
D) $$\sqrt{12}$$
E) −12

Kudos for a correct solution.

Source: Chili Hot GMAT

suppose V=1, the first operation results in 1-(1/2)=1/2; the second operation results in (1/2)-(1/4)= 1/4
If 1/4 is the final result, V=1
If 3 is the final result, V=12
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Posts: 22
Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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V*=3-----------(1)

Then
(V-V/2)* = (V-V/2)-((V-V/2)/2)
=((2v-v)/2) - ((2v-v)/4)
=(4v-2v-2v+v)/4--------(2)
From (1) and (2)
=>V/4=3
=>V=3x4=12

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Re: For all real numbers V, the operation V* is defined by the equation V*  [#permalink]

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Hello from the GMAT Club BumpBot!

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_________________ Re: For all real numbers V, the operation V* is defined by the equation V*   [#permalink] 13 Sep 2018, 05:30
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