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

 It is currently 18 Nov 2019, 23:16

### 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

# Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]

Author Message
TAGS:

### Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

Updated on: 09 Oct 2015, 23:36
1
2
00:00

Difficulty:

95% (hard)

Question Stats:

27% (01:44) correct 73% (01:37) wrong based on 67 sessions

### HideShow timer Statistics

Suppose x is an integer such that $$(x^2 - x - 1)^ {(x+2)} =1$$ . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

http://www.GMATinsight.com

_________________
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 09 Oct 2015, 22:14.
Last edited by GMATinsight on 09 Oct 2015, 23:36, edited 1 time in total.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

09 Oct 2015, 22:15
GMATinsight wrote:
Suppose x is an integer such that $$(x^2 - x - 1)^ {(x+2)} =1$$ . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

http://www.GMATinsight.com

$$(x^2 -x-1)^ {(x+2)} =1$$ is possible only when

Either (x ^ 2 -x-1)=1 i.e. x = 2 or -1

OR (x+2) =0 i.e. x = -2

OR x=0

i.e. Possible values of x = 0, 2, -1 and -2

_________________
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
Intern
Joined: 30 May 2014
Posts: 15
WE: Information Technology (Consulting)
Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

10 Oct 2015, 02:50
By substituting the values, -2,-1,0,2

CEO
Joined: 20 Mar 2014
Posts: 2570
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

10 Oct 2015, 05:29
GMATinsight wrote:
GMATinsight wrote:
Suppose x is an integer such that $$(x^2 - x - 1)^ {(x+2)} =1$$ . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

http://www.GMATinsight.com

$$(x^2 -x-1)^ {(x+2)} =1$$ is possible only when

Either (x ^ 2 -x-1)=1 i.e. x = 2 or -1

OR (x+2) =0 i.e. x = -2

OR x=0

i.e. Possible values of x = 0, 2, -1 and -2

There is another case of when base = exponent = 1 at the same time as $$1^{any integer} = 1$$

Based on the graph attached, the 2 curves show 3 points of intersections. 0 is not a point of intersection.

Attachment:

graph.png [ 10.34 KiB | Viewed 1213 times ]
Board of Directors
Joined: 17 Jul 2014
Posts: 2497
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

05 Dec 2015, 12:51
I highly doubt you will see such a question on the real GMAT.
but just my 2 cents
the whole expression is equal to 1 only in case it is equal to 1, or equal to -1, but then x must be even.

first case:
(x^2-x-1)=1
x(x-1)=2
x can be 2
x can be -2
x can be -1

second case:
(x^2-x-1) = -1.
x(x-1)=0
x-1=0
x=0
x-1=0 => x=1. can't be, since (x^2-x-1)^(x+2) will not yield a positive answer.
x=0 - satisfies the condition.

again, I don't think gmat will give such a question.
Non-Human User
Joined: 09 Sep 2013
Posts: 13604
Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

### Show Tags

12 Nov 2019, 20:49
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: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]   [#permalink] 12 Nov 2019, 20:49
Display posts from previous: Sort by