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# Is k^2 + k – 2 > 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Is k^2 + k – 2 > 0?  [#permalink]

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29 Oct 2017, 01:03
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:57) correct 34% (01:24) wrong based on 76 sessions

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Is k^2 + k – 2 > 0?

(1) k < 1
(2) k > –1

_________________
Manager
Joined: 21 Jun 2014
Posts: 62
Re: Is k^2 + k – 2 > 0?  [#permalink]

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29 Oct 2017, 02:30
For expression to be positive Either K > 1 or K < -2
Option C

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Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: Is k^2 + k – 2 > 0?  [#permalink]

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29 Oct 2017, 03:06
1
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k < 1
(2) k > –1

Hi...

Let's simplify the equation

$$k^2+k-2>0.........k^2+2k-k-2>0......k(k+2)-1(k+2)>0.....(k+2)(k-1)>0$$..
So both k+2 and k-1 should be of same SIGN..
So a)k between -2 and 1 will give us and NO
b) K<-2 and k>1 will give us and YES

Let's see the statements..
1) k<1...
It will give us falling in both above ranges, so ans can be yes or no
Insufficient
2) k>-1
Same as above
K=0 will give us no
K=5 will give YES
Insufficient

Combined
-1<k<1
This range falls within (a) above
ANS is always NO
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 01 Nov 2017
Posts: 29
Re: Is k^2 + k – 2 > 0?  [#permalink]

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28 Jun 2018, 08:42
chetan2u wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k < 1
(2) k > –1

Hi...

Let's simplify the equation

$$k^2+k-2>0.........k^2+2k-k-2>0......k(k+2)-1(k+2)>0.....(k+2)(k-1)>0$$..
So both k+2 and k-1 should be of same SIGN..
So a)k between -2 and 1 will give us and NO
b) K<-2 and k>1 will give us and YES

Let's see the statements..
1) k<1...
It will give us falling in both above ranges, so ans can be yes or no
Insufficient
2) k>-1
Same as above
K=0 will give us no
K=5 will give YES
Insufficient

Combined
-1<k<1
This range falls within (a) above
ANS is always NO
Sufficient

C

I don't understand this. Doesn't the formula simplify to the following
1) k^2 + k - 2 > 0
2) k^2 + k > 2
3) k(k+1) > 2
4) k > 2 and k > 1 => So K must be greater than 1 to be more than 0
Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: Is k^2 + k – 2 > 0?  [#permalink]

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28 Jun 2018, 09:16
surfingpirate wrote:
chetan2u wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(1) k < 1
(2) k > –1

Hi...

Let's simplify the equation

$$k^2+k-2>0.........k^2+2k-k-2>0......k(k+2)-1(k+2)>0.....(k+2)(k-1)>0$$..
So both k+2 and k-1 should be of same SIGN..
So a)k between -2 and 1 will give us and NO
b) K<-2 and k>1 will give us and YES

Let's see the statements..
1) k<1...
It will give us falling in both above ranges, so ans can be yes or no
Insufficient
2) k>-1
Same as above
K=0 will give us no
K=5 will give YES
Insufficient

Combined
-1<k<1
This range falls within (a) above
ANS is always NO
Sufficient

C

I don't understand this. Doesn't the formula simplify to the following
1) k^2 + k - 2 > 0
2) k^2 + k > 2
3) k(k+1) > 2
4) k > 2 and k > 1 => So K must be greater than 1 to be more than 0

By doing this you are missing out on the negative values...
It is not mentioned that k is positive..

For example if k =-3...
K(k+1)>2...
-3(-3+1)=-3*-2=6>2
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 01 Nov 2017
Posts: 29
Re: Is k^2 + k – 2 > 0?  [#permalink]

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28 Jun 2018, 11:57
C[/quote]

I don't understand this. Doesn't the formula simplify to the following
1) k^2 + k - 2 > 0
2) k^2 + k > 2
3) k(k+1) > 2
4) k > 2 and k > 1 => So K must be greater than 1 to be more than 0[/quote]

By doing this you are missing out on the negative values...
It is not mentioned that k is positive..

For example if k =-3...
K(k+1)>2...
-3(-3+1)=-3*-2=6>2[/quote]
I see. I tested the negative case so ending up figuring that out. How would you represent the negative instance algebraically? Like k(k+1) > 2 (positive) and k(k+1) < -2 (negative)?
Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: Is k^2 + k – 2 > 0?  [#permalink]

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28 Jun 2018, 21:39
surfingpirate wrote:
C

I don't understand this. Doesn't the formula simplify to the following
1) k^2 + k - 2 > 0
2) k^2 + k > 2
3) k(k+1) > 2
4) k > 2 and k > 1 => So K must be greater than 1 to be more than 0
Quote:
By doing this you are missing out on the negative values...
It is not mentioned that k is positive..

For example if k =-3...
K(k+1)>2...
-3(-3+1)=-3*-2=6>2

I see. I tested the negative case so ending up figuring that out. How would you represent the negative instance algebraically? Like k(k+1) > 2 (positive) and k(k+1) < -2 (negative)?

hi..

you are not taking k(k+1)<-2..

you are working on the same equation..
k(k+1)>2..
but here k can take both negative values and positive values...

if k>0, k will have to be greater than 1... so k>1 fulfills the criteria
if k<0, k will have to be less than -2.... so k<-2 also fulfills the criteria
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: Is k^2 + k – 2 > 0? &nbs [#permalink] 28 Jun 2018, 21:39
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