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# Find the integer K: (1) K*|K|=4 (2) |K|*|K|=4

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Find the integer K: (1) K*|K|=4 (2) |K|*|K|=4 [#permalink]  06 Jun 2003, 03:52
Find the integer K:

(1) K*|K|=4
(2) |K|*|K|=4
Manager
Joined: 03 Jun 2003
Posts: 84
Location: Uruguay
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I also go with A

In A only chance is 2
In B either 2 or -2 work
Senior Manager
Joined: 22 Nov 2005
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stolyar wrote:
A is correct

Can someone explain Why A

My logic is

K*|K| = 4

so |K| = +K if K > 0
= -K if K < 0

case 1 K > 0:

K * |K| = K * K = 4 ---> K^2 = 4 ---> K = +/- 2

Since K has two values so its not possible.

For case 2 K < 0

|K| = -k

==> K* (-k) = -K^2 = 4 -->>> which doesn't make any sense.

Can someone point out flaw in my derivation
Manager
Joined: 04 Jan 2006
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stmt 1:
K*|k| =4
K has to be +2.

if k = -2, then k*|k| = -2*|-2| = -2*2 = -4
So stmt 1 is suff to know K = 2

stmt2:
|k|*|k| = 4
Here K can be +2 or -2. Both will result in 4.
So insuff.
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Joined: 07 Jul 2004
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Location: Singapore
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gmat_crack wrote:
stolyar wrote:
A is correct

Can someone explain Why A

My logic is

K*|K| = 4

so |K| = +K if K > 0
= -K if K < 0

case 1 K > 0:

K * |K| = K * K = 4 ---> K^2 = 4 ---> K = +/- 2

Since K has two values so its not possible.

For case 2 K < 0

|K| = -k

==> K* (-k) = -K^2 = 4 -->>> which doesn't make any sense.

Can someone point out flaw in my derivation

You're right that -K^2 = 4, but we know if we solve it, the result would be an imaginary number. Since the GMAT does not take imaginary numbers as a legitimate answer, st1 is deemed to be sufficient.
Manager
Joined: 30 Jan 2006
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gmat_crack wrote:
stolyar wrote:

My logic is

K*|K| = 4

so |K| = +K if K > 0
= -K if K < 0

Can someone point out flaw in my derivation

Are you stating the following in your logic?:

so |K| = -K if K < 0

If yes, then that's where the flaw is... the absolut value of any given number can never be negative, only positive! Therefore, your statement "|K| = -K if K < 0" is incorrect.

Think of the absolute value of a given number as the "steps" it is away from zero. For example, -2 is two steps away from zero. Thus |-2| = 2.

The rest of the explanation is perfectly given by Nayan.
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stolyar wrote:
Find the integer K:

(1) K*|K|=4
(2) |K|*|K|=4

from i, if k = -2, K*|K|= -4 which is not true.
if k = 2, K*|K|= 4 which is true. so the only possible value of k =2.

from ii, if k = 2, K*|K|= 4 which is true.
if k = -2 2, K*|K|= 4 which is also true. so here k can be + or - 2.

so only A is sufficient.

gmat_crack wrote:
stolyar wrote:
A is correct

Can someone explain Why A
My logic is
K*|K| = 4
so |K| = +K if K > 0
= -K if K < 0
case 1 K > 0:
K * |K| = K * K = 4 ---> K^2 = 4 ---> K = +/- 2
Since K has two values so its not possible.
For case 2 K < 0
|K| = -k
==> K* (-k) = -K^2 = 4 -->>> which doesn't make any sense.
Can someone point out flaw in my derivation
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