Last visit was: 01 May 2026, 17:55 It is currently 01 May 2026, 17:55
Home
Messages
Tests
Schools
Events
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
655-705 (Hard)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 110,001
Own Kudos:
812,337
 [10]
Given Kudos: 105,976
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: 110,001
Kudos: 812,337
 [10]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 16 Mar 2021, 01:30
Kudos
Add Kudos
9
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:

65% (hard)

Question Stats:

53% (01:44) correct 47% (01:54) wrong based on 125 sessions

History

Date
Time
Result
Not Attempted Yet
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

(2) \(x ≠ −16\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 110,001
Own Kudos:
812,337
 [1]
Given Kudos: 105,976
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: 110,001
Kudos: 812,337
 [1]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 17 Mar 2021, 01:15
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k = 0\), where k is a constant, and x is a variable.

(2) \(x ≠ −16\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
Show more

If x^2+12x−k=0, is x=4?

(1) (x+16) is a factor of x^2+12x−k=0, where k is a constant, and x is a variable. This implies that we can factor out \(x+16\) from \(x^2+12x-k=0\), so we would have \((x+16)*(something)=0\). Thus x=-16 is one of the roots of the given quadratic equation.

Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).

Thus according to the above \(x_1+x_2=-16+x_2=\frac{-12}{1}\) --> \(x_2=4\).

So, we have that x is either -16 or 4. Not sufficient.

(2) x≠−16. Clearly insufficient.

(1)+(2) Since (2) says that x is NOT -16, then x=4. Sufficient.

Answer: C.

Hope it's clear.
General Discussion
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 01 May 2026
Posts: 587
Own Kudos:
1,191
 [1]
Given Kudos: 14
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 740 Q51 V39
Expert
Expert reply
GMAT 1: 740 Q51 V39
Posts: 587
Kudos: 1,191
 [1]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 16 Mar 2021, 02:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

(2) \(x ≠ −16\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
Show more


x^2 + 12x − k = 0
Sum of roots = -12
Product of roots = -k

From statement 1:
(x + 16) is a factor => x = -16 is a root
Since sum of roots is -12, the other root must be 4
Thus:
x^2 + 12x − k = (x - 4)(x + 16) = 0
=> x = 4 or 16
Thus, x may be 4 or 16 - insufficient


Alternative approach:
x = -16 is a root
Substitute x = -16 in given equation:
(-16)² + 12(-16) - k = 0
k = 256 - 192 = 64

x^2 + 12x − k
x^2 + 12x − 64 = (x - 4)(x + 16) = 0
=> x = 4 or 16
Thus, x may be 4 or 16 - insufficient


From statement 2:
Clearly this is insufficient since we don't know the value of k

Combining:

x = 4 (since it is not -16)
Sufficient

Answer C

Posted from my mobile device
User avatar
bidskamikaze
User avatar
Joined: 07 Jan 2018
Last visit: 29 Oct 2022
Posts: 251
Own Kudos:
308
 [2]
Given Kudos: 160
Location: India
Schools: ESMT NUS '22 IIMA PGPX'23 NTU
GMAT 1: 710 Q49 V38
Schools: ESMT NUS '22 IIMA PGPX'23 NTU
GMAT 1: 710 Q49 V38
Posts: 251
Kudos: 308
 [2]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 16 Mar 2021, 04:43
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

(2) \(x ≠ −16\)

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
Show more

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.
put x=-16 in the equation, we get k=64

The equation becomes: \(x^2 + 12x − 64 = 0\)
Solving this equation, we get \((x-4)(x+16)=0 \)
i.e, \(x=4\) or \(x=-16\)
We can't be sure what x is, as we have 2 values.
INSUFFICIENT.

(2) \(x ≠ −16\)
By itself, this option doesn't tell whether \(x=4\)
INSUFFICIENT

COMBINE 1) and 2):
From 1) we have \(x=4\) or \(x=-16\)
From 2) we have \(x ≠ −16\)

Therefore \(x=4\)
SUFFICIENT.

ANSWER C.
avatar
TarunKumar1234
avatar
Joined: 14 Jul 2020
Last visit: 28 Feb 2024
Posts: 1,102
Own Kudos:
1,358
 [1]
Given Kudos: 351
Location: India
Posts: 1,102
Kudos: 1,358
 [1]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 16 Mar 2021, 09:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x^2+12x−k=0, is x=4?

Stat1: (x+16) is a factor of x^2+12x−k, where k is a constant, and x is a variable.

Putting x = -16 in the equation, x^2+12x−k= 0 or, 256- 192 -k =0 or, k= 64.
Now, equation, x^2+12x−64 =0so, x = -16 or 4. No idea, which is the value of x to consider. Not sufficient.

Stat2: x≠−16; But, we don't know value of k, so we can't be sure, if x = 4. Not sufficient.

Combining both, x = 4. Sufficient.

So, I think C. :)
avatar
Kyala1Jameson
avatar
Joined: 09 Mar 2021
Last visit: 11 Jul 2021
Posts: 28
Own Kudos:
30
 [1]
Given Kudos: 25
Location: South Africa
Concentration: Leadership, Marketing
Schools: LBS MAM "23
GPA: 3.01
WE:Design (Computer Software)
Schools: LBS MAM "23
Posts: 28
Kudos: 30
 [1]
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 16 Mar 2021, 11:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
imo C
If \(x^2 + 12x − k = 0\), is \(x = 4\)?

(1) \((x + 16)\) is a factor of \(x^2 + 12x − k\), where k is a constant, and x is a variable.

\(x^2 + 12x − k\)
if X=-16 ,k =64
so X =4 as well .As we have 2 values of X
Not sufficient


(2) \(x ≠ −16\)
No idea about k .. or X ..
Not sufficient


Combinig .. we can get that
if \(x ≠ −16\)
x will be 4

sufficient
C is the ans
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,014
Own Kudos:
1,122
Posts: 39,014
Kudos: 1,122
If x^2 + 12x − k = 0, is x = 4? (1) (x + 16) is a factor of x^2 + 12x 22 Mar 2022, 10:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110001 posts
kingbucky
498 posts
Gmat860sanskar
215 posts