Sep 19 12:00 PM PDT  10:00 PM PDT On Demand $79, For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Sep 19 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction. Sep 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day Data Sufficiency & Critical Reasoning workshop and learn the best strategies to tackle the two trickiest question types in the GMAT! Sep 21 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Sep 22 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58092

If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
27 Mar 2017, 03:54
Question Stats:
61% (01:52) correct 39% (02:24) wrong based on 201 sessions
HideShow timer Statistics
If \(x^1 + x^{(−1)} = 5\), what is the value of \(x^4 + x^{(−4)}\)? A. 527 B. 546 C. 579 D. 600 E. 625
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2819

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
29 Mar 2017, 10:10
Bunuel wrote: If x^1 + x^(−1) = 5, what is the value of x^4 + x^(−4)?
A. 527 B. 546 C. 579 D. 600 E. 625 We are given that x^1 + x^(−1) = 5, i.e., x + 1/x = 5. We need to determine the value of x^4 + x^(4), i.e., x^4 + 1/x^4. Let’s square both sides of the equation x + 1/x = 5.: (x + 1/x)^2 = 5^2 x^2 + 2(x)(1/x) + 1/x^2 = 25 x^2 + 2 + 1/x^2 = 25 x^2 + 1/x^2 = 23 Now let’s square the above equation: (x^2 + 1/x^2)^2 = 23^2 x^4 + 2(x^2)(1/x^2) + 1/x^4 = 529 x^4 + 2 + 1/x^4 = 529 x^4 + 1/x^4 = 527 Answer: A
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Senior Manager
Joined: 19 Apr 2016
Posts: 271
Location: India
GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
27 Mar 2017, 04:26
Bunuel wrote: If x^1 + x^(−1) = 5, what is the value of x^4 + x^(−4)?
A. 527 B. 546 C. 579 D. 600 E. 625 \(x^1 + x^{(−1)} = 5\)  I \((x+1/x)^2 = x^2 + 1/x^2 + 2\) \(5^2 = x^2 + 1/x^2 + 2\) (by using I) \(x^2 + 1/x^2 = 23\)  II \((x^2+1/x^2)^2 = x^4 + 1/x^4 + 2\) \(23^2 = x^4 + 1/x^4 + 2\) (by using II) \(x^4 + 1/x^4 = 529  2 = 527\) Hence option A is correct Hit Kudos if you liked it



Intern
Joined: 21 Mar 2017
Posts: 37
Location: Zimbabwe
Concentration: General Management, Entrepreneurship
GMAT 1: 680 Q45 V38 GMAT 2: 750 Q49 V42
GPA: 3.3
WE: Accounting (Accounting)

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
13 Sep 2017, 04:05
Official Answer Direct attempts to solve for x in this problem will run into quadratics that don't factor and horrible nonintegers that need to be raised to fourth powers. Instead, let's focus on manipulating the equation to solve for x^4 + x^−4 directly. Given the similar structure of the given information, it seems reasonable to begin by squaring the equation x^1+x^−1=5. Be careful, though, not to simply square each term; exponents do not distribute over addition. Instead, recognize the special quadratic. We're looking at two terms added and then squared, so this expression fits the form (a+b)^2=a^2+2ab+b^2. Thus our result will be (x^1+x^−1^2=5^2 (x^1)^2+2(x^1)(x^−1)+(x^−1)^2=25 x^2+2+x^−2=25 x^2+x^−2=23 Now just repeat the process of squaring both sides once more: (x^2+x^−2)^2=23^2 x^4+2(x^2)(x^−2)+x^−4=23^2 x^4+2+x^−4=23^2 x^4+x^−4=23^2−2 And it's not even really necessary to calculate 23^2 (which turns out to be 529). 23^2 must end in a 9, so 23^2−2 must end in a 7, and the answer has to be A.
_________________
Kudos if you like my response please



Intern
Joined: 26 Dec 2016
Posts: 29

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
05 Jan 2018, 22:46
JeffTargetTestPrep wrote: Bunuel wrote: If x^1 + x^(−1) = 5, what is the value of x^4 + x^(−4)?
A. 527 B. 546 C. 579 D. 600 E. 625 We are given that x^1 + x^(−1) = 5, i.e., x + 1/x = 5. We need to determine the value of x^4 + x^(4), i.e., x^4 + 1/x^4. Let’s square both sides of the equation x + 1/x = 5.: (x + 1/x)^2 = 5^2 x^2 + 2(x)(1/x) + 1/x^2 = 25 x^2 + 2 + 1/x^2 = 25 x^2 + 1/x^2 = 23 Now let’s square the above equation: (x^2 + 1/x^2)^2 = 23^2 x^4 + 2(x^2)(1/x^2) + 1/x^4 = 529 x^4 + 2 + 1/x^4 = 529 x^4 + 1/x^4 = 527 Answer: A why do we need to square it? In the response below your original post, it says that "it's reasonable" to do. Can you explain please? Thanks



Retired Moderator
Joined: 25 Feb 2013
Posts: 1191
Location: India
GPA: 3.82

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
05 Jan 2018, 22:57
rnz wrote: JeffTargetTestPrep wrote: Bunuel wrote: If x^1 + x^(−1) = 5, what is the value of x^4 + x^(−4)?
A. 527 B. 546 C. 579 D. 600 E. 625 We are given that x^1 + x^(−1) = 5, i.e., x + 1/x = 5. We need to determine the value of x^4 + x^(4), i.e., x^4 + 1/x^4. Let’s square both sides of the equation x + 1/x = 5.: (x + 1/x)^2 = 5^2 x^2 + 2(x)(1/x) + 1/x^2 = 25 x^2 + 2 + 1/x^2 = 25 x^2 + 1/x^2 = 23 Now let’s square the above equation: (x^2 + 1/x^2)^2 = 23^2 x^4 + 2(x^2)(1/x^2) + 1/x^4 = 529 x^4 + 2 + 1/x^4 = 529 x^4 + 1/x^4 = 527 Answer: A why do we need to square it? In the response below your original post, it says that "it's reasonable" to do. Can you explain please? Thanks Hi rnzwe are given \(x^1+x^{1}\) and need to arrive at \(x^4+x^{4}\). So squaring the original equation will raise it to power of \(2\) i.e. \(x^2+x^{2}\) and on further squaring this expression we will reach our destination



Intern
Joined: 30 Oct 2017
Posts: 8

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
06 Jan 2018, 15:54
Can someone please explain how we arrive at (x^2+1/X^2+2)?
(x+1/x)^2 = (x^2+1/X^2+2)?



Retired Moderator
Joined: 25 Feb 2013
Posts: 1191
Location: India
GPA: 3.82

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
06 Jan 2018, 20:20
mekoner wrote: Can someone please explain how we arrive at (x^2+1/X^2+2)?
(x+1/x)^2 = (x^2+1/X^2+2)? Hi mekonerthere is a very simple formula used here \((a+b)^2=a^2+b^2+2ab\) now instead of \(a\) & \(b\) use \(x\) & \(\frac{1}{x}\) here



NonHuman User
Joined: 09 Sep 2013
Posts: 12371

Re: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
Show Tags
13 Jul 2019, 23:06
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: If x^1+x^(−1)=5, what is the value of x^4+x^(−4)?
[#permalink]
13 Jul 2019, 23:06






