Last visit was: 14 Jul 2025, 21:57 It is currently 14 Jul 2025, 21:57
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
User avatar
Bismuth83
User avatar
DI Forum Moderator
Joined: 15 Sep 2024
Last visit: 14 Jul 2025
Posts: 724
Own Kudos:
2,042
 [7]
Given Kudos: 441
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 724
Kudos: 2,042
 [7]
Given the equation x^2kx+20=0 , where k is a constant, which of the 16 Oct 2024, 15:24
2
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide Answer
Hide
Show
History
k: 9 x: 4
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

72% (02:00) correct 29% (02:05) wrong based on 800 sessions

History

Date
Time
Result
Not Attempted Yet
Given the equation \(x^2−kx+20=0\), where \(k\) is a constant, which of the following could be corresponding values of integers \(k\) and \(x\)?­
k x
-20
-9
-2
0
4
9
Submit Answer
Start the Timer above, select the radio buttons, and click "Submit" to add this question to your Error log.
User avatar
poojaarora1818
User avatar
Joined: 30 Jul 2019
Last visit: 14 July 2025
Posts: 1,501
Own Kudos:
697
Given Kudos: 3,138
Location: India
Concentration: General Management, Economics
Schools: Duke '26 Haas '26 Kelley '26 Kellogg '26 McDonough '26
GPA: 3
WE:Human Resources (Human Resources)
Schools: Duke '26 Haas '26 Kelley '26 Kellogg '26 McDonough '26
Posts: 1,501
Kudos: 697
Given the equation x^2kx+20=0 , where k is a constant, which of the 17 Oct 2024, 06:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bismuth83
Given the equation \(x^2−kx+20=0\), where \(k\) is a constant, which of the following could be corresponding values of integers \(k\) and \(x\)?­
Solution: x^2 -kx+20 = 0

We have to factorize and find two solutions for x. Here you go:


(x-4) (x-5) = 0

We know x could be either 4 or 5. Now, as per the value given to us the value for x is 4.

We can put this value into the equation x^2 -kx+20 = 0 and have the value for constant K is 9.

Hence, the answer is x= 4 and K = 9
User avatar
naveeng15
User avatar
Joined: 08 Dec 2021
Last visit: 23 Jun 2025
Posts: 72
Own Kudos:
9
Given Kudos: 38
Location: India
Concentration: Operations, Leadership
GMAT 1: 610 Q47 V28
WE:Design (Manufacturing)
GMAT 1: 610 Q47 V28
Posts: 72
Kudos: 9
Given the equation x^2kx+20=0 , where k is a constant, which of the 17 Oct 2024, 06:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Use quadratic qns to solve qn
User avatar
Bismuth83
User avatar
DI Forum Moderator
Joined: 15 Sep 2024
Last visit: 14 Jul 2025
Posts: 724
Own Kudos:
2,042
 [1]
Given Kudos: 441
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 724
Kudos: 2,042
 [1]
Given the equation x^2kx+20=0 , where k is a constant, which of the 17 Oct 2024, 10:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bismuth83
Given the equation \(x^2−kx+20=0\), where \(k\) is a constant, which of the following could be corresponding values of integers \(k\) and \(x\)?­

1. We are asked to find what could be k and x in this equation.

2. The first idea is to use the quadratic formula: \(x_{1,2} = \frac{k \pm \sqrt{k^2 - 80}}{2}\).

3. Since the square root takes only nonnegative numbers, \(k^2 - 80 \geq 0 \rightarrow k^2 \geq 80 \rightarrow |k| \geq \sqrt{80}\). Looking at the answer choices, k is whole, so \(|k| \geq \sqrt{81} = 9\). The only possible answer choices are k = -20 and \(\pm\)9.

4. It can also be noticed that \(\sqrt{k^2 - 80}\) must be whole for x to be whole too. \(\pm\)9 work, however, if k = -20 then \(\sqrt{k^2 - 80} = \sqrt{400 - 80} = \sqrt{320} = 8\sqrt{5}\), which isn't whole. So, only \(\pm\)9 could work.

5. Plugging k = -9 gives the roots -5 and -4, while k = 9 gives 5 and 4. Only 4 is a possible x.

6. Our answer will be k = 9 and x = 4.

__________________________________

Another way of excluding all options except k = -20 and \(\pm\)9 is by drawing out the two graphs \(x^2 + 20\) and \(kx\). They should be equal and it's easy to realize that k has to be large (absolute value) for the two graphs to intersect.
User avatar
poojaarora1818
User avatar
Joined: 30 Jul 2019
Last visit: 14 July 2025
Posts: 1,501
Own Kudos:
697
Given Kudos: 3,138
Location: India
Concentration: General Management, Economics
Schools: Duke '26 Haas '26 Kelley '26 Kellogg '26 McDonough '26
GPA: 3
WE:Human Resources (Human Resources)
Schools: Duke '26 Haas '26 Kelley '26 Kellogg '26 McDonough '26
Posts: 1,501
Kudos: 697
Given the equation x^2kx+20=0 , where k is a constant, which of the 17 Oct 2024, 10:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
naveeng15
Use quadratic qns to solve qn
Yes, I knew the quadratic Equations formula to solve this ques but the only problem is that it consumes a lot of time to solve the ques and get to the solution. My apologies. Next, time I will take care of these steps to provide a solution. Thanks for the advice though.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 14 Jul 2025
Posts: 11,294
Own Kudos:
41,744
 [4]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,294
Kudos: 41,744
 [4]
Given the equation x^2kx+20=0 , where k is a constant, which of the 23 Oct 2024, 09:40
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bismuth83
Given the equation \(x^2−kx+20=0\), where \(k\) is a constant, which of the following could be corresponding values of integers \(k\) and \(x\)?­
A very quick method and a method not getting into quadratic equations will be..

\(x^2−kx+20=0......x(x-k)=-20=-1×20=-2×10=-4×5\)

The products that are in options..
1. -20 : x(x-k) = 1×-20 ... This would require k to be -21....-20×(-20-(-21))
21 is not in the options.

2. -2 : x(x-k) = -2×10... This would require k to be -12....-2×(-2-(-12))
10 is not in the options.

3. 4 : x(x-k) = 4×-5 ... This would require k to be 9....4×(4-9).... We have both 4 and 9 in the options.

Thus x=4 & k=9
Moderator:
Bunuel
Math Expert
102570 posts