If k is a positive constant and y = |x - k| - |x + k|, what is the maximum value of y?
(1) x < 0
(2) k = 3
(1) x < 0
(2) k = 3
Im not sure I am right.
IMO B
If that is right I will explain my answer.
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Maximum value of y
Source: Beat The GMAT — Data Sufficiency |
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
-
- Graph of y = |x - k| + |x+k|
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Well I guess he explained it for you. By the way thanks for showing the graphing way to do it. Much easier.
Thanks Karmayogi!
Thanks Karmayogi!
