NEW HERE? LEARN MORE
closeclose
It is currently 23 Apr 2024, 07:19
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

14 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92860
CAT Tests Forum Quiz Mode
Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  06 Dec 2018, 05:36
2
Kudos
16
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

57% (01:56) correct 43% (01:51) wrong based on 534 sessions
Hide Show timer Statistics
Is K an even number ?


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

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


M36-45

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
request expert reply
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92860
CAT Tests Forum Quiz Mode
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  27 Oct 2021, 00:17
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
Is K an even number ?


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

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


M36-45



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
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
P
DavidTutorexamPAL
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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!
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User CAT Tests
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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.
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User CAT Tests
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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]"
User avatar
P
DavidTutorexamPAL
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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?
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User CAT Tests
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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..
User avatar
P
DavidTutorexamPAL
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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.).
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User CAT Tests
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92860
CAT Tests Forum Quiz Mode
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  24 Dec 2018, 01:18
Expert Reply
Bunuel wrote:
Is K an even number ?


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

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


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


_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
B
aru010
Intern
Intern
Joined: 19 Nov 2017
Posts: 11
Location: Singapore
Concentration: Technology, Entrepreneurship
Schools: Duke '22 (D) Kellogg '22 (D) Melbourne '21 (A$) Owen '22 (A$) Cornell Tech "21 (A$) Rotman '22 (A$) Schulich(Jan) '22 (A)
GMAT 1: 590 Q45 V27
GMAT 2: 700 Q48 V37
GPA: 3.44
WE:Engineering (Computer Software)
Reviews Badge
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  24 Dec 2018, 17:56
1
Kudos
(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)
User avatar
B
rahul12988
Intern
Intern
Joined: 07 Apr 2018
Posts: 47
Location: India
Schools: INSEAD Jan'21 Intake MBS '22 (A) Oxford "21 (WA) Cass '21 (A)
GMAT 1: 690 Q48 V39
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  21 Jul 2019, 10:24
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
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5342
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  08 Oct 2019, 05:02
Bunuel wrote:
Is K an even number ?


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

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


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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32618
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink] New post  05 Jul 2023, 14:22
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: Is K an even number ? (1) |K - |K|| = K + |K| (2) K^(1/2) = K [#permalink]
05 Jul 2023, 14:22
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
92859 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions