Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K

Question

Is K an even number ?

(1) |K - |K|| = K + |K|

(2)  \sqrt K=K

M36-45

Bunuel · Accepted Answer

Official Solution:

Is  K  an even number ?
 
(1)  |K - |K|| = K + |K| 
 
When  K \leq 0 , so when  |K| = -K , the expression transforms into  |K - (-K)| = K + (-K) , which leads to  |2K| = 0 . This gives  K = 0 ; 
 
When  K > 0 , so when  |K| = K , the expression transforms into  |K - K| = K + K , which leads to  |0| = 2K . This gives  K = 0 ; 
 
Sufficient.
 
(2)  \sqrt K=K 
 
Square to get rid of the square root:  K = K^2 ;
 
 K(K-1)=0 ;
 
 K=0  and  K=1 
 
Not sufficient.

Answer: A

DavidTutorexamPAL · Answer

The answer is A. 
 1) This is true only for 0. 
(any positive number will give 0 on the left side and a positive number on the right. and negative number will give a positive number on the left and 0 on the right). 
Sufficient! 
2) this is true for both x=0 (an even number) and x=1 (an odd number). insufficient!

Archit3110 · Answer

from 1 : given relation stands true only at K = 0 so sufficient

from 2 sqrtk= sqrt k* sqrtk
or 1=sqrtk 
we get k =+/-1 so in sufficient IMO A is correct.

Archit3110 · Answer

@DavidTutorexamPAL

for stament 2:
sqrtk = k is given
and we can say
sqrtk= sqrtk * sqrtk

OR
1=sqrtk
or k= +/-1 .. which is in sufficient..
I am not sure why have you said that  "2) this is true for both x=0 (an even number) and x=1 (an odd number). insufficient! "

DavidTutorexamPAL · Answer

"

Not sure I understand the question... 
The equation in 2) is indeed true for 1 and -1, as you mention, but it is also true for 0 (root0=0). Thus, k can be either even (0) or odd (1, -1), and this statement is insufficient. 
Is this clearer?

Archit3110 · Answer

Not sure I understand the question... 
The equation in 2) is indeed true for 1 and -1, as you mention, but it is also true for 0 (root0=0). Thus, k can be either even (0) or odd (1, -1), and this statement is insufficient. 
Is this clearer?

DavidTutorexamPAL :
Yes i did get that it would be true for both 0, +/-1 .. what I meant was that if you simplify stmt 2 you would get k = +/-1 only .. not 0 ..

In DS my approach is usually to simplify the given relation than plug in values..

anyways statement 2 is in sufficient ... thanks for replying..

DavidTutorexamPAL · Answer

Ok, now I understand. 
This is not true - and in fact, would cause a mistake! 
Remember, when simplifying, we can never divide or multiply by a variable which may be 0. in this case, doing so makes us miss that x=0 is a possible solution as well. (which in turn should actually make us select D, since 1 and -1 are both odd.).

Archit3110 · Answer

DavidTutorexamPAL  : OK I understood your point .. thanks

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

aru010 · Answer

(1) |K - |K|| = K + |K|

(2) √K‾‾=K

Simplifying (2), squaring both sides 
k = k*k => k(k-1)=0 so k=1 or k =0 not sufficient

Simplifying(1)
for k>0 
 |k-k| = k+k => 0 = 2k => k=0

For k< 0 
 |k+k| = 0 => k=0 sufficient

hence (A)

rahul12988 · Answer

For B 
K = 0 or 1 NS
For A ( i used 2 approaches )
|K - |K|| = K + |K|
if I remove this modulus i will get K -|K| = K+|K| 
2|K|= 0 then K=0
or K -|K| = -(K+|K|)
2K=0 
both equations are giving K= 0 then A is sufficient 
I am not sure whether my approach for A is right because number plugging was quick approach

Kinshook · Answer

Asked: Is K an even number ?

(1) |K - |K|| = K + |K| 
K = 0
SUFFICIENT

(2)  \sqrt K=K [
K = 0 or 1
NOT SUFFICIENT

IMO A

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards