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GMAT Exam  >  GMAT Questions  >  For all real numbers v, the operation is defi... Start Learning for Free
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
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For all real numbers v, the operation is defined by the equation v* = ...
Solution:

Let's solve this problem step by step.

Step 1: Define the operation "v*"
The operation "v*" is defined by the equation v* = v - v/3.

Step 2: Find (v*)*
To find (v*)*, we need to substitute v* into the equation for v. So, (v*)* = (v*) - (v*)/3.

Step 3: Simplify (v*)*
To simplify (v*)*, we need to substitute the expression for v* into the equation. Therefore, (v*)* = (v - v/3) - (v - v/3)/3.

Step 4: Simplify the equation
Simplifying the equation further, we have (v*)* = v - v/3 - (v - v/3)/3.

Step 5: Simplify the right side of the equation
Simplifying the right side of the equation, we have (v*)* = v - v/3 - (v/3 - v/9).

Step 6: Continue simplifying
Continuing to simplify, we have (v*)* = v - v/3 - v/3 + v/9.

Step 7: Simplify further
Further simplification gives (v*)* = v - 2v/3 + v/9.

Step 8: Simplify even more
Continuing to simplify, we have (v*)* = v - (2v/3 - v/9).

Step 9: Simplify the right side
Simplifying the right side, we have (v*)* = v - (6v/9 - v/9).

Step 10: Simplify further
Further simplification gives (v*)* = v - 5v/9.

Step 11: Simplify the equation
Finally, we have (v*)* = v - 5v/9 = 8.

Step 12: Solve for v
To solve for v, we need to solve the equation v - 5v/9 = 8.

Step 13: Simplify the equation
Simplifying the equation, we have (9v - 5v)/9 = 8.

Step 14: Solve for v
Solving for v, we have 4v/9 = 8.

Step 15: Simplify further
Simplifying further, we have 4v = 72.

Step 16: Solve for v
Solving for v, we have v = 72/4 = 18.

Therefore, the value of v is 18, which corresponds to option B.
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Community Answer
For all real numbers v, the operation is defined by the equation v* = ...
To find the value of v, we need to substitute the given equation and solve for v.
The operation v* is defined as v* = v - v/3.
We are given that (v*)* = 8.
Substituting the definition of v* into the equation, we have:
(v*)* = (v - v/3) - (v - v/3)/3
Simplifying the expression, we get:
(v*)* = (v - v/3) - v/3 + v/9
(v*)* = v - v/3 - v/3 + v/9
(v*)* = v - 2v/3 + v/9
(v*)* = (9v - 6v + v)/9
(v*)* = 4v/9
Since (v*)* is equal to 8, we can set up the equation:
4v/9 = 8
To solve for v, we multiply both sides of the equation by 9/4:
v = 8 * (9/4)
v = 18
Therefore, the value of v is 18. Hence, the correct answer is option B.
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For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v =a)15b)18c)21d)24e)27Correct answer is option 'B'. Can you explain this answer?
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