If k is a positive constant and y = |x - k| - |x + k|, what

Question

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

mikemcgarry · Accepted Answer

Dear faceharshit , I'm happy to respond. :-)

First of all, here are some more practice questions you may find helpful. https://magoosh.com/gmat/2013/gmat-quant ... qualities/ Here, let's pull back and think about this. The numbers (x - k) and (x + k) are points on the number line separated by a distance of 2k. Now, depending on the way we subtract, the difference might be +2k or -2k, and the absolute values will get tricky when x is close to zero where (x - k) and (x + k) have opposite signs. Clearly, the value of k will be important in establishing an answer. What's a little unclear is x. Does x have a single unknown numerical value? In that case, the expression y would have a single value. There would be no question of a "maximum" value. The fact that the question is asking for a "maximum" value implies that x moves over a range. Statement #1 : x < 0 We have no information about the value of k, and we would need that to give any sort of answer. This is insufficient . Statement #2 : k = 3 We have to assume that x would equal any real number. If x is a large negative number, say x = -20, then y = (-20 - 3) - (-20 + 3) = -23 - (-17) = +6 When x is closer than 3 to zero on either side, the value of y is less. For example, when x = 0, y = 0. Now consider a large positive value, say, x = +20. y = (20 - 3) - (20 + 3) = 17 - 23 = -6 Thus, the maximum value of y is +6. (Notice that this is 2k.) We have a definitive answer. Thus, statement #2, alone and by itself, is sufficient . Answer = (B) Does this make sense? Mike :-)

jlgdr · Answer

Pretty straightforward

Since we want the maximum value of 'y' and knowing that |x - k| is always >=0, we wan't |x + k| = 0, thus x= -k in order to have min 'y'

Statement 1 only says that x<0 but still not information on the exact value
Statement 2 gives that k=3, therefore x=-3 and we can solve min 'y' having the value of both variables

Therefore answer is B

Hope this clarifies
Cheers!
J

blueseas · Answer

IMO its E

BECAUSE
AS PER STATEMENT 2
y=|x-3|+|x+3|

NOW IT TOTALLY DEPENDS ON X..

I THINK QUESTION SHOULD BE
y=|x-k| - |x+k|

mau5 · Answer

Please type the question carefully. For the given question, the answer would be E.

The original question reads as y=|x-k|-|x+k|.

From F.S 1, we know that x<0.

From the image, the last 2 cases correspond to this scenario. In one of the cases, the value of y would be 2k, and in the other case, the value would be less than 2k. However, we don't know the value of k, thus Insufficient.

From F.S 2, we know that only if x<-k, can we get the maximum value of y as 2k = 2*3  = 6. Sufficient.

B.

Transcendentalist · Answer

y=|x-k|-|x+k|

Statement 1 x<0

y = -x+k - |x+k| The second term could be -x-k, 0 or x+k depending on k Insufficient'

Statement 2 k = 3

y = |x+3| - |x-3|

Lets consider various instances

x< 0

x = -100 x<-k

y = 97 - 103 = -6 (Please note the value remains the same for x = 10000 also)

x = -2 , -k<x<0

y = 1 - 5 = -4

x = 0

y = 3 - 3 = 0

x>0

x = 100 x>k

y = 103 - 97 = 6 (Please note the value remains the same for x = 10000 also)

x = 2 , 0>x>k

y = 5 - 1 = 4

Hence max value of y is 6.. Ans B

Observer · Answer

Since y can be positive for any k, then the maximum value of y will be positive. When y is positive |x-k|-|x+k| = ||x-k|-|x+k|| <= |x-k-x-k| = 2k. So the maximum is 2k. We need k.

1. Doesn't tell us k. Insufficient.
2. Tells us k. Sufficient.
B.

Asifpirlo · Answer

this problem has theoretical problem i think, by explaining differently we can change the result.

faceharshit · Answer

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

How to proceed solving this ?

Bunuel · Answer

Merging similar topics. Please refer to the solutions above and ask if anything remains unclear. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 1 and 3. Thank you.

StrikerT · Answer

Hey All,

What if we had k=4 as option A? Would the answer be A.

My question is if the value of K changes, the max value will change too? Kindly suggest.

Thanks in advance.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

There is one variable (k) and 2 equations are given by the 2 conditions, so there is high chance (D) will be our answer.
For condition 1, we cannot determine the value for k, so this is insufficient.
For condition 2, in y=|x-3|-|x+3|
when x<-3, y=6
when -3<=x<3, y=2x
when 3<=x, y=-6
The maximum value is always 6, so this is unique and sufficient.
The answer becomes (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

If k is a positive constant and y = |x - k| - |x + k|, what

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GMAT Data Sufficiency (DS) Questions

If k is a positive constant and y = |x - k| - |x + k|, what

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