Manhattan GMAT 700+ Challenge Problem - Absolute

is it D..not very sure..

the answer is E...

A is not sufficient because we need the value of K
B is not sufficient because we need the value of X

Combining A & B. Since the value of X is less than 0, X could be -1, -2, and so on..

Let's try -1 for x
y=lx-kl - lx+kl
y=l-1-3l - l-1+3l
y=l-4l - l2l
y= 2

Let's try -2 for x
y=lx-kl - lx+kl
y=l-2-3l - l-2+3l
y=l-5l - l1l
y= 4

We can see that the value of y varies. So the answer is E.

E

y = mod(x-k) - mod(x+k)

3 cases

k>x
y = -2x
k<x
y = -2k
k=x
y = -2x


1) x<0
gives y>2*mod(x) and y < -2k

2) k = 3
y = -2k = -6
y= -2x (where -2x would be > -6)

in either case we do not know x
even upon considering 1)and 2) together, we do not know x

so E

quite tough
but answer is E
oops i didnt read it carefully earlier.
ok if its max it has to be B.

i think its statement 2 only wat u say?

wats the real answer?

I'm getting B. The maximum seems to max out at 6. Let us know, quite curious. These types of q's are the most difficult for me.

Answer
(1) INSUFFICIENT: Statement (1) is insufficient because y is unbounded when both x and k can vary. Therefore y has no definite maximum.

To show that y is unbounded, let's calculate y for a special sequence of (x, k) pairs. The sequence starts at (-2, 1) and doubles both values to get the next (x, k) pair in the sequence.

y1 = | -2 – 1 | – | -2 + 1 | = 3 – 1 = 2
y2 = | -4 – 2 | – | -4 + 2 | = 6 – 2 = 4
y3 = | -8 – 4 | – | -8 + 4 | = –12 + 4 = 8
etc.

In this sequence y doubles each time so it has no definite maximum, so statement (1) is insufficient.

(2) SUFFICIENT: Statement (2) says that k = 3, so y = | x – 3 | – | x + 3 |. Therefore to maximize y we must maximize | x – 3 | while simultaneously trying to minimize | x + 3 |. This state holds for very large negative x. Let's try two different large negative values for x and see what happens:

If x = -100 then:
y = |-100 – 3| – |-100 + 3|
y = 103 – 97 = 6

If x = -101 then:
y = |-101 – 3| – |-101 + 3|
y = 104 – 98 = 6

We see that the two expressions increase at the same rate, so their difference remains the same. As x decreases from 0, y increases until it reaches 6 when x = –3. As x decreases further, y remains at 6 which is its maximum value.

The correct answer is B.

On a number line the points will be like this

-------- -k --------0----------k----------

For y to have maximum value x needs to be either equal to or less than -k

y is max when x<=-k

y = 2k

We need k value to find the answer for y

B is sufficient.

Thanks
Raama

nice one kevin!!