Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
09 Aug 2014, 03:56
Question Stats:
28% (02:15) correct 72% (01:59) wrong based on 345 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 Kudos for correct solution
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”




Tutor
Joined: 20 Apr 2012
Posts: 97
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38
WE: Education (Education)

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
09 Aug 2014, 04:32
For the equation (x^2−x−1)\(^{(x+2)}\)=1 to be true, there are three possibilities: 1. \((x^2x1) =1\) \(x^2x2=0\)> \(x=2\) or \(x=1\). Both roots are possible. So, we have 2 values. 2. \((x^2x1) =1\) and (x+2) is even\(x^2x=0\)>\(x=1\) or \(x=0\). Check if \(x+2\) is even: if \(x=1\), then \(x+2odd\); if \(x=0\), then \(x+2even\). So only \(x=0\) is possible. +1 value. 3. x+2=0 and \((x^2x1)\neq=0\) . Therefore, x=2. +1 value Hence 4 values: 2, 1, 0, 2 D.
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos:)




Manager
Status: Applied
Joined: 02 May 2014
Posts: 125
Location: India
Concentration: Operations, General Management
Schools: Tulane '18 (A), Tippie '18 (D), Moore '18, Katz '18 (D), UCSD '18, Madison '18, Olin '18 (S), Simon '18, Desautels '18 (I), Sauder '18 (S), Terry '18 (WL), GWU '18, Neeley '18 (WL), Weatherhead '18 (S), Fox(Temple)'18, Eller FT'18 (A), Schulich Sept"18 (S)
GPA: 3.35
WE: Information Technology (Computer Software)

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
24 Dec 2014, 05:00
x=0 is 1st solution. x+2=0 implies x=2 second solution x^2x1=1 implies x^2x2=0 implies x=2 and x=1 another 2 solutions so total 4 solutions.



Manager
Joined: 03 Jan 2015
Posts: 58
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
01 Feb 2015, 10:42
smyarga wrote: For the equation (x^2−x−1)\(^{(x+2)}\)=1 to be true, there are three possibilities:
1. \((x^2x1) =1\) \(x^2x2=0\)> \(x=2\) or \(x=1\). Both roots are possible. So, we have 2 values.
2. \((x^2x1) =1\) and (x+2) is even \(x^2x=0\)>\(x=1\) or \(x=0\). Check if \(x+2\) is even: if \(x=1\), then \(x+2odd\); if \(x=0\), then \(x+2even\). So only \(x=0\) is possible. +1 value.
3. x+2=0 and \((x^2x1)\neq=0\) . Therefore, x=2. +1 value
Hence 4 values: 2, 1, 0, 2
D. Hi,
How did you get (x^2x1) to equal "1"?
TO



Senior Manager
Joined: 13 Jun 2013
Posts: 266

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
01 Feb 2015, 13:34
thorinoakenshield wrote: Hi,
How did you get (x^2x1) to equal "1"?
TO
if (x^2x1) is equal to 1, then (x+2) must be even. why ?? because (1)^2n = 1 here n can take values of 0,1,2,3,,, etc



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
01 Feb 2015, 15:51
Hi thorinoakenshield, We're given (X^2  X  1)^(X+2) = 1 Given the way that the prompt is written, there are several ways to get a total that = 1: (1)^(any power) = 1 (1)^(even power) = 1 (any number)^0 = 1 The 'second option' is arguably the most 'complex' because it depends on 2 things (the base = 1 AND the exponent is EVEN). IF.... (X^2  X  1) = 1 X^2  X = 0 X(X  1) = 0 This equation has 2 solutions: 0 and 1. HOWEVER, only one of them fits the given prompt.... IF.... X = 0, we have (1)^(0+2) = 1, so this is a valid solution. IF.... X = 1, we have (1)(1+3) = 1 > this is NOT a valid solution, since the end result is NOT 1. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 06 May 2014
Posts: 11

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
16 Sep 2015, 19:59
EMPOWERgmatRichC wrote: Hi thorinoakenshield,
We're given (X^2  X  1)^(X+2) = 1
Given the way that the prompt is written, there are several ways to get a total that = 1:
(1)^(any power) = 1 (1)^(even power) = 1 (any number)^0 = 1
The 'second option' is arguably the most 'complex' because it depends on 2 things (the base = 1 AND the exponent is EVEN).
IF.... (X^2  X  1) = 1 X^2  X = 0 X(X  1) = 0
This equation has 2 solutions: 0 and 1. HOWEVER, only one of them fits the given prompt....
IF.... X = 0, we have (1)^(0+2) = 1, so this is a valid solution.
IF.... X = 1, we have (1)(1+3) = 1 > this is NOT a valid solution, since the end result is NOT 1.
GMAT assassins aren't born, they're made, Rich what will be the ans? a or d?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
16 Sep 2015, 23:10
anik1989 wrote: what will be the ans? a or d? The answer is (D) There are 4 values x can take: 2, 1, 0, 2 (look at smyarga's solution above)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 06 May 2014
Posts: 11

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
17 Sep 2015, 04:55
VeritasPrepKarishma wrote: anik1989 wrote: what will be the ans? a or d? The answer is (D) There are 4 values x can take: 2, 1, 0, 2 (look at smyarga's solution above) thank you karishma. honestly i dod not get that ans. why power has been ignored in sloution??



Intern
Joined: 28 May 2013
Posts: 19

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
20 Sep 2015, 01:07
anik1989 wrote: VeritasPrepKarishma wrote: anik1989 wrote: what will be the ans? a or d? The answer is (D) There are 4 values x can take: 2, 1, 0, 2 (look at smyarga's solution above) thank you karishma. honestly i dod not get that ans. why power has been ignored in solution?? Hi Anik1989, No power has been ignored in the solution. As smyarga mentioned there are three possibilities. 1) Base is 1, then irrespective of the power, answer will be 1. Thus by equating base =1, we get values of x=2, x=1. Now if we substitute these values in main equation (base^power), equation holds true. Thus we have 2 values of x 2) Base is 1 and power is even number. Then answer will always be 1. Now by equating base to 1, we get x=1,x=0. However, as per our condition if x=1, the power(x+2) becomes odd, thus only x=0 can be taken as a true value. So we have 1 value from this condition. 3) if power is zero(0) then, irrespective of the base, answer will be 1. Thus, by equating power(x+2) to 0, (x+2)=0, x=2 thus we have totally 4 values(2,1,0,2) from all the three above conditions. Hence answer is D. Hope it clears your doubt. Power is not ignored, in fact, every possibility is considered! Cheers Tx



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
21 Sep 2015, 22:49
anik1989 wrote: VeritasPrepKarishma wrote: anik1989 wrote: what will be the ans? a or d? The answer is (D) There are 4 values x can take: 2, 1, 0, 2 (look at smyarga's solution above) thank you karishma. honestly i dod not get that ans. why power has been ignored in sloution?? Ok, first think about this: \(a^b = 1\) In which all cases can this happen? Case 1: a = 1, b can be anything e.g. \(1^4\), \(1^{3}\), \(1^0\) Case 2: a = 1, b must be an even integer e.g. \((1)^2\), \((1)^{4}\) Case 3: b = 0, a must be a non zero number. e.g. 2^0 So you evaluate each one of these three cases: Case 1: a = 1, b can be anything \(x^2−x−1 = 1\) \(x^2  x 2 = 0\) \(x^2  2x + x  2 = 0\) \((x + 1)(x  2) = 0\) x = 1 or 2 We don't need to worry about b. Case 2: a = 1, b must be an even integer \(x^2−x−1 = 1\) \(x(x  1) = 0\) x = 0 or 1 (x+2) must be even integer. If x = 0, (0+2) is an even integer. If x = 1, (1+2) is an odd integer so this is not valid. From this case, we get only one value of x i.e. 0. Case 3: b = 0, a must be a non zero number. (x+2) = 0 x = 2 If x = 2, \(x^2−x−1\) is not 0. So this is a valid solution too. We got four solutions: x = 1, 2, 0, 2
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



NonHuman User
Joined: 09 Sep 2013
Posts: 13264

Re: Suppose x is an integer such that (x^2−x−1)^(x+2)=1
[#permalink]
Show Tags
31 Mar 2018, 12:21
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 (x^2−x−1)^(x+2)=1
[#permalink]
31 Mar 2018, 12:21






