Im not sure I am right.
IMO B
If that is right I will explain my answer.
Maximum value of y
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Source: Beat The GMAT — Data Sufficiency |
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karmayogi
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IMO B.
There are two ways to solve the problem.
1. By observation
y = |x - k| - |x + k|
For k = +ve
y< 0 for x > k
y>0 for x< k
The value will be maximum when |x+k| = 0. Therefore for x = -k, y = 2k, which is the maximum value.
2. Above is not a fool proof method, but a quick one. The best solution is drawing graph.
First draw the graph of y = x - k and y = x + k
Second draw the graph of y = |x-k| and y = |x+k|
Second graph will give you some idea. You can solve the problem from here itself. However, we can go step ahead and draw the actual graph of
y = |x - k| - |x + k|
The graph is attached with the post. Given value of K we can find the maximum value of y.
PS: you can also draw the final graph directly by plotting the values of x and assuming some constant value for k.
There are two ways to solve the problem.
1. By observation
y = |x - k| - |x + k|
For k = +ve
y< 0 for x > k
y>0 for x< k
The value will be maximum when |x+k| = 0. Therefore for x = -k, y = 2k, which is the maximum value.
2. Above is not a fool proof method, but a quick one. The best solution is drawing graph.
First draw the graph of y = x - k and y = x + k
Second draw the graph of y = |x-k| and y = |x+k|
Second graph will give you some idea. You can solve the problem from here itself. However, we can go step ahead and draw the actual graph of
y = |x - k| - |x + k|
The graph is attached with the post. Given value of K we can find the maximum value of y.
PS: you can also draw the final graph directly by plotting the values of x and assuming some constant value for k.
- Attachments
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- Graph of y = |x - k| + |x+k|
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