For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

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GMAT Paper Tests

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

OA B

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GMAT Paper Tests

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

OA B

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 have v* = 12, or:

v - v/3 = 12

2v/3 = 12

v = 12 x 3/2 = 18

Answer: B