Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 13:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56277
Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 05:36
1
2
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:57) correct 47% (01:47) wrong based on 149 sessions

### HideShow timer Statistics

Is K an even number ?

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

(2) $$\sqrt K=K$$

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:01
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!
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:22
Bunuel wrote:
Is K an even number ?

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

(2) $$\sqrt K=K$$

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.
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:24
DavidTutorexamPAL wrote:
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!

@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![/quote]"
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:30
Archit3110 wrote:
DavidTutorexamPAL wrote:
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!

@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!
"[/quote]

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?
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:33
DavidTutorexamPAL wrote:
Archit3110 wrote:
DavidTutorexamPAL wrote:
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!

@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!
"

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?[/quote]

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..
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:42
Archit3110 wrote:
[quote=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..

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.).
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

06 Dec 2018, 06:46
DavidTutorexamPAL wrote:
Archit3110 wrote:
[quote=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..

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.).

DavidTutorexamPAL : OK I understood your point .. thanks
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Math Expert
Joined: 02 Sep 2009
Posts: 56277
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

24 Dec 2018, 01:18
Bunuel wrote:
Is K an even number ?

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

(2) $$\sqrt K=K$$

_________________
Intern
Joined: 19 Nov 2017
Posts: 12
Location: Singapore
Concentration: Technology, Entrepreneurship
GMAT 1: 590 Q45 V27
GPA: 3.44
WE: Engineering (Computer Software)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K  [#permalink]

### Show Tags

24 Dec 2018, 17:56
(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)
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K   [#permalink] 24 Dec 2018, 17:56
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne