If k is a positive constant and y = |x – k| – |x + k|, what is the maximum value of y? (Contributed by JR)
(1) x < 0
(2) k = 3
A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D) Each statement alone is sufficient to answer the question.
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
(E)
not enough info for |x+k| to be positive or negative value.
Yeah! i think its E too…
Not enough DATA! to find one sure shot value for y…
Let me know!
shobz.puppie@gmail.com
Shobhit Bhargava
b
yeah i too think b will be sufficient… max value of Y ll be 6…
How is the value 6 Basant? I think it is not enough of information.
B is enought
with statement 1 you have a broad number for x that will come possitives and a broad numbers for K both possitives and negatives
with statement 2 the formula will come:
y = |x-3| – |x+3|
trying with possitives for x will give you different negatives answers, but trying with 0 and and negatives all the answers will come to 6 as a maximun possibility.
Jorge (Peru – South America)
Answer is E. B wont be the answer because 6 will be the maximum possibility only if the equation was y= |x-3| + |x+3|.
E. Can we have also add our analysis everytime we post our answer.. something like “Jorge” did ?.. others can benefit
Basically if we consider the points in the no line then the question will be very simple. Here |x-k| is the difference between the points x and k. Similarly |x+k| is the difference between x and -k.
So to max the value of y, x has to be on the left of -k. In that case the value of Y will be difference between k & -k, & that will be the max value of y.
Now the 1st statement tells X<0 but it is not specifying any fixed value.
So we can’t deduce anything.
2nd statement says that k=3. but in this case it is not specifying any value of x. so if x -k, then max value will be <6. So we can’t answer.
Even if we take both the statements, then also we have no clue.
So ans is E.
I think it’s B. I just wanted to give my opinion on Siddhartha’s comment.
If the question was asking for just value of y, it is different for different values of x. Here the question is to find out the maximum value of y considering all the values of x.
This is indeed 6 when k=3. The minimum value of y is -6. Considerin all possible values for x, it cannot be more than 6 for y.
Just plot a graph for the equation (y=|x-3|-|x+3|) for x from -10 to 10 and y from -10 to 10 at this link http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=graphs&s2=equations&s3=basic.
I think its E. The value is dependent on whether abosolute value of x is bigger or smaller than K
how i came up with 6?? here’s d ans..
now as we hv to find the maximum value of y; we hv to make |x – k| greater than |x + k|… and to make the max possible difference x should be negative as k is positive.
taking k=3 acc to option b..
now keep trying possible values for x…
say x=0; then we hv y=0
now say x=-1; then we hv y=2
say x=-100; then we hv y=6
this is the maximum value of x… try taking other values of x as well…
Hope this helps…
I think the correct answer is B. Here if we take negative value for x ie x <= -3 then we get value for y as 6 which is maximum value.
c
i think the answer here is B as the maximum value of Y is refered to.
GMAT team plz comment.
It should be “A”
and the ans. is 2K.
yes A
Ans is B … for any value of x > -2 Y takes only 6 …
y= | x-3 | – | x+3 |
for x=-1 y=2
x=-2 y=4
x=-3 y=6
x=-4 y=6
so for any value less than -2 we have y=6 and thats the max vlaue i can take … So ans B
Ans C
e
Srry guys the answer is C
In any case you cannot answer the Q “what is the maximum value of y?”. This question is asking the exact maximum number.
So ans is E.
I made a mistake….maximum value would be 6 if we use both the data.
So ans is C
B
Because
if you go on plugging in the value from positve to negative x= 5, 4, 3,2, 1, 0,-1 , -2 , -3 ….and so on you will see a final value of +6 coming as the maximum value.
for Ix-kI -Ix+I
can have four option if Ix-kI and Ix+kI are one positive other neg.
next One neg other positive
next both positive
or both Neg. The results of these are -2k,2k,o,2x
then to find the biggest value we need both value of X and K
so the answer is C
x is positive: y = -2.k
x is negative: y = 2.k
So always need (2) to get y. Question asks for MAX y, which is always 2k, so don’t need (1).
Gmat team…. time to comment..!
pl.
B . The max value is 6.
It seems the answer is B but can someone please explain the quick way of solving it as we cannot waste imp. 5 min calculating all values of x during exam. Can we?
B. Max value is -6, if I am not wrong.
Official Answer is B.
B…
B
Let us explicit y depending on the value of x:
x-k>0 if x>k then |x-k|=x-k
x-k<0 if x0 if x>-k then |x+k|=x+k
x+k<0 if x<-k then |x+k|=-(x+k)=-k-x
Let us draw a axis line with indicating marks –k and k
-k +k
| |
|x-k|= -x+k 2k -x+k 0 x-k
|x+k|= -x-k 0 x+k -2k x+k
y=|x-k|-|x+k| 2k 2k -2x 2k -2k
(1) x<0 then there are 2 possible values 2k and -2x but cannot tell the greatest
So statement (1) alone is not sufficient
(2) k=3 then there are 3 possible values -6, -2x and 6 and cannot tell the greatest
So statement (29 alone is not sufficient
(1)+(2) there are 2 possible values 6 and -2x and cannot tell the greatest
So both statement together are sufficient
So the correct answer is E
GMAT Team could you please explain Ans (B)…
Agreed that the value of k is given. Putting in the equation x cancels out. But if we have to find the maximum value, should we not plug in different values of x to find the correct maximum?