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Director
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If k is a positive constant and y = |x - k| - |x + k|, what [#permalink]
 23 May 2006, 02:34
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
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Director
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I go with B.
The maximum value we get is 6 whatever the value of x
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SVP
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remgeo wrote: I go with B.
The maximum value we get is 6 whatever the value of x
Answer should be E,
Take X =1
=> |1-3| - |1+3|
=> 2 - 4
=> -2
Take x=0
=> |0-3| - |0+3|
=> 3 - 3
=> 0
Hence E
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Senior Manager
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Agree with B
There are four cases:
1) y = -2k
2) y = -2x
3) y = 2x
4) y = 2k
Since we are looking for the maximum value (1) is out immediately since
it's less then (4). Now , considering (2), -k < x < k , so (4) is still the winner here. In (3) , x > k and x < -k is impossible since k is positive by definition. So (4) is the biggest possible value.
Since B provides the value of k , we can find y. y = 2 * 3 = 6
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jaynayak wrote: remgeo wrote: I go with B.
The maximum value we get is 6 whatever the value of x Answer should be E, Take X =1 => |1-3| - |1+3| => 2 - 4 => -2 Take x=0 => |0-3| - |0+3| => 3 - 3 => 0 Hence E jaynayax,
(1) says that x<0
Agree with b. The max value of y is 2k
I choose C.
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deowl wrote: Agree with B
There are four cases:
1) y = -2k
2) y = -2x
3) y = 2x
4) y = 2k
Since we are looking for the maximum value (1) is out immediately since
it's less then (4). Now , considering (2), -k < x < k , so (4) is still the winner here. In (3) , x > k and x < -k is impossible since k is positive by definition. So (4) is the biggest possible value.
Since B provides the value of k , we can find y. y = 2 * 3 = 6
Deowl, can you go back a step and explain how you came up with the 4 cases? I got B as well, but I did the problem in a more lengthy, plug in numbers type of way.
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Intern
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How do you get 6 as a max? I'm getting 0
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tl372 wrote:
Deowl, can you go back a step and explain how you came up with the 4 cases? I got B as well, but I did the problem in a more lengthy, plug in numbers type of way.
1) x-k > 0, x+k > 0 => y=-2k, x > k, x > -k
2) x-k < 0, x+k > 0 => y=-2x, x < k , x > -k
3) x-k > 0, x+k < 0 => y=2x, x > k, x < -k
4) x-k < 0, x+k < 0 => y=2k, x < k, x < -k
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Re: MHTN Challenge [#permalink]
23 May 2006, 07:09
BG wrote: 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
C it is...
If x = -1 Y = 2
If X= -2 Y= 4
If X= -3 Y = 6
If X= -4 Y = 6
....
Y can not be over 6
hence, C
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oops....so B...not C 
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