GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 13:39

### 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

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 k² + k – 2 > 0?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445
Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 03:18
00:00

Difficulty:

65% (hard)

Question Stats:

61% (01:41) correct 39% (01:33) wrong based on 244 sessions

### HideShow timer Statistics

Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Is k² + k – 2 > 0?  [#permalink]

### Show Tags

Updated on: 23 Jul 2015, 03:57
1
1
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Question : Is k^2 + k – 2 > 0?
i.e. Question : Is k^2 + 2k - k – 2 > 0?
i.e. Question : Is (k + 2) (k - 1) > 0?

i.e. Question : Is k < -2 OR k > 1?

Statement 1: k is an integer greater than zero.
@k=1, (k + 2) (k - 1) is NOT greater than 0
@k=2, (k + 2) (k - 1) is greater than 0
NOT SUFFICIENT

Statement 2: k divided by 2 is an integer.
i.e. k is an Even Number
so k can be 0 or 2 or 4 etc. hence,
NOT SUFFICIENT

Combining the two statements:
i.e. k is an Even Number greater than zero
so k can be 2 or 4 or 6 etc
and for all values of k now (k + 2) (k - 1) is greater than 0
SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 23 Jul 2015, 03:44.
Last edited by GMATinsight on 23 Jul 2015, 03:57, edited 2 times in total.
CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 03:48
1
1
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Is k^2 + k – 2 > 0? -----> (k-1)(k+2) ---> is k>1 or k<-2

Per statement 1, k>0 . Now this value of k can be 1 (so k>1 is not true) but if k =3 , then yes k >1. As this statement is not a definite yes or no , this is not a sufficient statement.

Per statement 2, k/2 = integer ---> k = even integer = ...-2,0,2,4,6... etc . So is k<-2 or k>1 can be both yes or no per this statement. Hence this statement is not sufficient.

Combining, we get, k>0 and thus k =2,4,6,8.... ----> (k-1)(k+2) > 0 , a definite yes. Thus, C is the correct answer.
CEO
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 03:50
1
GMATinsight wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Question : Is k^2 + k – 2 > 0?
i.e. Question : Is k^2 - 2k + k – 2 > 0?
i.e. Question : Is (k - 2) (k + 1) > 0?

GMATinsight, given equation is k^2+k-1 and not k^2-k+1. The red part above is incorrect.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 03:58
Engr2012 wrote:
GMATinsight wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Question : Is k^2 + k – 2 > 0?
i.e. Question : Is k^2 - 2k + k – 2 > 0?
i.e. Question : Is (k - 2) (k + 1) > 0?

GMATinsight, given equation is k^2+k-1 and not k^2-k+1. The red part above is incorrect.

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04-01-2015
GPA: 3.98
Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 06:22
1
Our Question is
$$k^2+k-2>0 ?$$

Restate the given as $$k^2+2k-1k-2>0$$ ------> $$(k-1)(k+2)>0$$ ---------> k > 1 or k > -2

So our question now is Is k>1 or k> -2 ?

Statement 1 --- k > 0

Take k = 1 we get No
k = 2 we get Yes
So Not Sufficient

Statement 2 --- $$\frac{k}{2}$$ = Integer our in other words k can be even

Take k = 2 we get Yes
Take k = -2 we get No
So Not Sufficient

Together 1 + 2 we get
K is even and k > 0

So It is sufficient and answer is C
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks
Director
Joined: 21 May 2013
Posts: 636
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

23 Jul 2015, 06:57
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Statement 1: k is an integer>0
Given: (k-1)(k+2)>0 ?
Put k=1, equation=0
Put k=2, equation>0. Insufficient

Statement 2: k divided by 2 is an integer. k could be 0,2,4,6 etc
Insufficient

Using both, k =2,4,6 etc.
Math Expert
Joined: 02 Sep 2009
Posts: 58445
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

26 Jul 2015, 12:41
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

800score Official Solution:

The first thing we need to do is factor k² + k – 2 into (k + 2)(k – 1). From these factors, we can see that the value of k² + k – 2 = 0 when k = -2 or 1.

When k > 1, both k + 2 and k – 1 will be positive, so the product of the two (the original expression) will be positive.

Similarly, when k is between -2 and 1, the product of the two expressions will be negative.

Finally, when k is less than -2, the product will be positive.

So we've learned that k² + k – 2 > 0 as long as k is greater than 1 or less than -2.

Statement (1) tells us that k is an integer greater than zero. This is not sufficient because k² + k – 2 > 0 when k is greater than 1, but it will equal zero when k is 1.

Statement (2) tells us k is an even integer. This is also insufficient, because all even integer values of k will make k² + k – 2 greater than zero except -2 and 0. k = -2 will make the expression equal to zero, and k = 0 will make the expression negative. (Remember: 0 is an even integer!)

Combined, the two statements are sufficient, because the only possible values for k are positive even numbers (2 or greater), all of which make k² + k – 2 > 0.

Since the statements are insufficient individually, but sufficient when combined, the correct answer is choice (C).
_________________
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4009
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

10 Nov 2017, 11:14
Top Contributor
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k is an integer greater than zero.
(2) k divided by 2 is an integer.

Kudos for a correct solution.

Target question: Is k² + k – 2 > 0?
This is a good candidate for rephrasing the target question.

What needs to happen in order for k² + k – 2 to be positive?
Factor to get: k² + k – 2 = (k + 2)(k - 1)
For (k + 2)(k - 1) to be positive, we need one of two scenarios:

Scenario A: (k + 2) and (k - 1) are both POSITIVE
For this to occur, k must be greater than 1

Scenario B: (k + 2) and (k - 1) are both NEGATIVE
For this to occur, k must be less than -2

In other words, for k² + k – 2 to be positive, it must be the case that EITHER k is greater than 1 OR k is less than -2
REPHRASED target question: Is it true that EITHER k is greater than 1, OR k is less than -2?

Once we've rephrased the target question, we can head to the two statements....

Statement 1: k is an integer greater than zero.
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 2, in which case the answer to the REPHRASED target question is YES
Case b: k = 1, in which case the answer to the REPHRASED target question is NO
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k divided by 2 is an integer
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 2, in which case the answer to the REPHRASED target question is YES
Case b: k = 0, in which case the answer to the REPHRASED target question is NO
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that k is positive
Statement 2 tells us that k divided by 2 is an integer.
In other words, k/2 must be a positive integer
Some possible values of k: 2, 4, 6, 8, . . .
In all of these cases, the answer to the REPHRASED target question is YES
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 13275
Re: Is k² + k – 2 > 0?  [#permalink]

### Show Tags

29 Nov 2018, 10:54
1
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.
_________________
Re: Is k² + k – 2 > 0?   [#permalink] 29 Nov 2018, 10:54
Display posts from previous: Sort by