Last visit was: 19 Nov 2025, 02:20 It is currently 19 Nov 2025, 02:20
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 Level|   Algebra|      
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,389
 [20]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,389
 [20]
If x + 1/x = 4, what is the value of x^2 + 1/x^2? Updated on: 24 Feb 2024, 10:52
Originally posted by MathRevolution on 24 Sep 2016, 22:46.
Last edited by Bunuel on 24 Feb 2024, 10:52, edited 3 times in total.
1
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

76% (01:09) correct 24% (02:16) wrong based on 497 sessions

History

Date
Time
Result
Not Attempted Yet
If \(x + \frac{1}{x} = 4\), what is the value of \(x^2 + \frac{1}{x^2}\)?

A. 10
B. 12
C. 14
D. 16
E. 18­
ShowHide Answer
Official Answer
C
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,514
Own Kudos:
5,728
 [3]
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert
Expert reply
Posts: 3,514
Kudos: 5,728
 [3]
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Sep 2016, 23:09
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
MathRevolution
(ex 12) (equation) If x+(1/x)=4, \(x^2+(1/x^2)\)=?
A. 10 B. 12 C. 14 D. 16 E. 18
Show more

x + 1/x = 4

Squaring both sides,

\((x + 1/x )^2 = 4^2\)

or \(x^2+(1/x^2) + 2 = 16\)

or \(x^2+(1/x^2) = 14\)

Hence, C
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,379
Own Kudos:
778,172
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,379
Kudos: 778,172
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 25 Sep 2016, 02:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
Show more

Similar question: if-x-2-1-x-2-4-what-is-the-value-of-x-4-1-x-175113.html
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,934
Own Kudos:
5,327
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,934
Kudos: 5,327
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 25 Sep 2016, 07:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
If \(x+\frac{1}{x}\) =4, \(x^2+\frac{1}{x^2}\)= ?

A. 10
B. 12
C. 14
D. 16
E. 18
Show more

\(x+\frac{1}{x}\) =4

\((x+\frac{1}{x})^2\) = \(4^2\) { Squaring both sides }

Or, \(x^2\) + \(2*x*\frac{1}{x}\)+ \(\frac{1}{x^2}\) = \(16\)

Or, \(x^2\) + \(2\) + \(\frac{1}{x^2}\) = 16

Or, \(x^2+\frac{1}{x^2}\) = \(16 - 2\)

Or, \(x^2+\frac{1}{x^2}\) = \(14\)

So, Answer will be C. 14
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,336
 [1]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,336
 [1]
If x + 1/x = 4, what is the value of x^2 + 1/x^2? Updated on: 25 May 2020, 12:53
Originally posted by BrentGMATPrepNow on 25 Sep 2016, 08:27.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:53, edited 1 time in total.
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
MathRevolution
If x + (1/x) = 4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
Show more

Given: x + (1/x) = 4

NOTE: since there are squared terms in the expression we're trying to evaluate, we should consider squaring both sides.

Square both sides: [x + (1/x)]² = 4²
Rewrite as: [x + (1/x)][x + (1/x)] = 16
Use FOIL method to expand: x² + 1 + 1 + 1/x² = 16
Simplify: x² + 2 + 1/x² = 16
Subtract 2 from both sides: x² + 1/x² = 14

Answer: C
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,389
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,389
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 27 Sep 2016, 09:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
Answer: C
User avatar
Arsh4MBA
User avatar
Joined: 19 Jul 2017
Last visit: 14 Oct 2017
Posts: 68
Own Kudos:
26
Given Kudos: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Posts: 68
Kudos: 26
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 17 Sep 2017, 07:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
Show more

(x+1/x)^2 = X^2+2+1/x^2;

So x^2+1/x^2 = 16- 2 = 14;

Ans:C
User avatar
pushkarajnjadhav
User avatar
Joined: 12 Feb 2017
Last visit: 30 Nov 2020
Posts: 59
Own Kudos:
90
Given Kudos: 48
Posts: 59
Kudos: 90
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 26 Sep 2017, 23:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x + 1/x = 4

Squaring both sides,

(x+1/x)^2 = 4^2

x^2+(1/x^2)+2*x*1/x=16
x^2+(1/x^2)+2=16
x^2+(1/x^2)=14
Hence Answer is option C.

Kudos if it helps.
User avatar
Salsanousi
User avatar
Joined: 19 Oct 2013
Last visit: 29 Dec 2020
Posts: 393
Own Kudos:
351
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Posts: 393
Kudos: 351
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 13 Oct 2018, 02:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
X + 1/x = 4

(x + 1/x)^2 = 4^2

x^2 + 2 (x * 1/x) + 1/x^2 = 16

x^2 + 2 + 1/x^2 = 16

x^2 + 1/x^2 = 16 - 2 = 14

ArjunJag1328 check the above it may clarify your question.

Posted from my mobile device
User avatar
KanishkM
User avatar
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 759
Own Kudos:
503
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Schools: DeGroote'21 Desautels '21 NUS '21
Posts: 759
Kudos: 503
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Jan 2019, 06:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})?\)

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)
Show more

Manipulate the if part as

\(x+(\frac{1}{x})^2=16\)

x^2 + 1/x^2 = 16 - 2

= 14

Answer C
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,934
Own Kudos:
5,327
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,934
Kudos: 5,327
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Jan 2019, 08:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})?\)

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)
Show more

\(x+(\frac{1}{x})=4\)

Squaring both sides we have -

\(x^2 + 2*x*\frac{1}{x} + \frac{1}{x^2} = 16\)

Or, \(x^2 + 2+ \frac{1}{x^2} = 16\)

Or, \(x^2 +\frac{1}{x^2} = 14\), Thus Answer must be (C)
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,389
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,389
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 27 Jan 2019, 18:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
=>

\(( x + \frac{1}{x} )^2 = x^2 + 2x(\frac{1}{x}) + (\frac{1}{x})^2 = x^2 + (\frac{1}{x})^2 + 2 = 4^2 = 16.\)
Thus, \(x^2 + (\frac{1}{x})^2 = ( x + \frac{1}{x} )^2 - 2 = 16 - 2 = 14.\)

Therefore, the answer is C.
Answer: C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,582
Own Kudos:
1,079
Posts: 38,582
Kudos: 1,079
If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Feb 2024, 11:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105379 posts
Krunaal
Tuck School Moderator
805 posts