GMAT Exam > GMAT Questions > If v* = (1/v), find the value ofv* + (v*)* + ...
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If v* = (1/v), find the value of
v* + (v*)* + ((v*)*)* if v = 1/2.
- a)3
- b)7/2
- c)4
- d)9/2
- e)5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If v* = (1/v), find the value ofv* + (v*)* + ((v*)*)* if v = 1/2.a)3b)...
Step 1: Question statement and Inferences
A function has been defined called v* such that v* = 1v
Step 2 & 3: Finding required values and calculating the final answer
v = 1/2
=> v*=1v=2
=> (v*)* = (2)* = 1/2
=> ((v*)*)* = (1/2)* = 2
=> v* + (v*)* + ((v*)*)* = 2 + 1/2 + 2 = 9/2.
Answer: Option (D)
Most Upvoted Answer
If v* = (1/v), find the value ofv* + (v*)* + ((v*)*)* if v = 1/2.a)3b)...
To find the value of v*, we substitute v = 1/2 into the equation v* = 1/v.
Given:
v = 1/2
Substituting this value into the equation v* = 1/v, we have:
v* = 1/(1/2)
= 1 * (2/1)
= 2
So, v* = 2.
Now, let's find the value of (v*)*.
Given:
v* = 2
To find (v*)*, we substitute v* = 2 into the equation v* = 1/v.
(v*)* = 1/(v*)
= 1/2
So, (v*)* = 1/2.
Next, let's find the value of ((v*)*)*.
Given:
(v*)* = 1/2
To find ((v*)*)*, we substitute (v*)* = 1/2 into the equation v* = 1/v.
((v*)*)* = 1/((v*)*)
= 1/(1/2)
= 1 * (2/1)
= 2
So, ((v*)*)* = 2.
Finally, we need to find the value of v* (v*)* ((v*)*)*.
Substituting the values we found:
v* (v*)* ((v*)*)* = 2 * (1/2) * 2
= 2 * 1/2 * 2
= 2
Therefore, v* (v*)* ((v*)*)* = 2.
Since v = 1/2, the correct answer is option 'D' (9/2).
Given:
v = 1/2
Substituting this value into the equation v* = 1/v, we have:
v* = 1/(1/2)
= 1 * (2/1)
= 2
So, v* = 2.
Now, let's find the value of (v*)*.
Given:
v* = 2
To find (v*)*, we substitute v* = 2 into the equation v* = 1/v.
(v*)* = 1/(v*)
= 1/2
So, (v*)* = 1/2.
Next, let's find the value of ((v*)*)*.
Given:
(v*)* = 1/2
To find ((v*)*)*, we substitute (v*)* = 1/2 into the equation v* = 1/v.
((v*)*)* = 1/((v*)*)
= 1/(1/2)
= 1 * (2/1)
= 2
So, ((v*)*)* = 2.
Finally, we need to find the value of v* (v*)* ((v*)*)*.
Substituting the values we found:
v* (v*)* ((v*)*)* = 2 * (1/2) * 2
= 2 * 1/2 * 2
= 2
Therefore, v* (v*)* ((v*)*)* = 2.
Since v = 1/2, the correct answer is option 'D' (9/2).
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