Last visit was: 23 Apr 2026, 01:04 It is currently 23 Apr 2026, 01:04
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,712
 [14]
Given Kudos: 105,850
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: 109,763
Kudos: 810,712
 [14]
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n 28 Mar 2023, 05:45
1
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
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:

70% (01:51) correct 30% (01:46) wrong based on 519 sessions

History

Date
Time
Result
Not Attempted Yet
What is the minimum value of \(f(n) = 2n^2 - 7n + 8\), if \(n\) is an integer?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 22 Apr 2026
Posts: 16,439
Own Kudos:
79,390
 [5]
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,439
Kudos: 79,390
 [5]
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n 03 May 2023, 02:48
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
HoudaSR
Bunuel
What is the minimum value of \(f(n) = 2n^2 - 7n + 8\), if \(n\) is an integer?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)


In order to minimize f(n)=2n^2 - 7n + 8, I would need to minimize 2n^2 - 7n as there is nothing I can do about 8, it is just a constant.

In order to minimize 2n^2 - 7n , it has to be less than 0
2n^2 - 7n < 0
Therefore 2n^2 must be less than 7n; which tells me that n has to be greater than 0 and less than 4

As I start picking values for n, I get the following:
For n=1; f(n)= 3
For n=2; f(n)= 2
For n=3 ; f(n)=5

Hence the minimum value of f(n)=2n^2 - 7n + 8 is 2.

Correct answer is B

Bunuel KarishmaB can you please check the reasoning followed above to solve this question and tell me if there are any flaws in it?
Thank you in advance for your feedback.
Show more

Use the same logic for f(n)=2n^2 - n + 8 and see what goes wrong.

This is how you can solve it instead:

The minimum value of a quadratic in x can be found at x = -b/2a if a is positive. Otherwise, at x = -b/2a, we get the maximum value.

So the minimum value of 2n^2 - n + 8 can be found at n = -b/2a = -(-7)/2*2 = 7/4 = 1.75
Since n must be an integer, the minimum value for any integer value of n will be at n = 2.

Attachment:
Screenshot 2023-05-03 at 3.15.07 PM.png
Screenshot 2023-05-03 at 3.15.07 PM.png [ 23.94 KiB | Viewed 4764 times ]
Look at the parabola in the diagram. The integer 2 is closest to 1.75 and since the parabola is symmetric about n = 1.75, its value at n = 1 will be greater than its value at n = 2.
at n = 2, f(n) = 2

Answer (B)
General Discussion
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 23 Apr 2026
Posts: 6,976
Own Kudos:
16,904
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,976
Kudos: 16,904
 [1]
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n Updated on: 22 Feb 2025, 01:14
Originally posted by GMATinsight on 28 Mar 2023, 06:07.
Last edited by Bunuel on 22 Feb 2025, 01:14, edited 3 times in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the minimum value of \(f(n) = 2n^2 - 7n + 8\), if \(n\) is an integer?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)
Show more

for n to be an integer we can simply substitute the values of n and find for what value is the f(n) minimum

@n = 0, \(f(n) = 2n^2 - 7n + 8 = 8\)
@n = 1, \(f(n) = 2*1^2 - 7*1 + 8 = 3\)
@n = 2, \(f(n) = 2*2^2 - 7*2 + 8 = 2\)

i.e. f(n) minimum = 2, @n=2

Answer: Option B

Please watch the following video for more mathematical explanation
User avatar
bv8562
User avatar
Joined: 01 Dec 2020
Last visit: 01 Oct 2025
Posts: 415
Own Kudos:
505
Given Kudos: 360
GMAT 1: 680 Q48 V35
GMAT 1: 680 Q48 V35
Posts: 415
Kudos: 505
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n 28 Mar 2023, 06:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATinsight
Bunuel
What is the minimum value of \(f(n) = 2n^2 - 7n + 8\), if \(n\) is an integer?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)

for n to be an integer we can simply substitute the values of n and find for what value is the f(n) minimum

@n = 0, \(f(n) = 2n^2 - 7n + 8 = 8\)
@n = 1, \(f(n) = 2*1^2 - 7*1 + 8 = 3\)
@n = 2, \(f(n) = 2*2^2 - 7*2 + 8 = 4\)

i.e. f(n) minimum = 3 @n=2

Answer: Option C
Show more
The result of the highlighted part must be 2. So, the correct answer must be B.
User avatar
HoudaSR
User avatar
Joined: 08 Aug 2022
Last visit: 24 Nov 2023
Posts: 72
Own Kudos:
48
Given Kudos: 181
Location: Morocco
Schools: HBS '26 Oxford Said'25 Judge '25 Rotterdam'25 Yale '24
WE:Advertising (Non-Profit and Government)
Schools: HBS '26 Oxford Said'25 Judge '25 Rotterdam'25 Yale '24
Posts: 72
Kudos: 48
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n 02 May 2023, 13:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the minimum value of \(f(n) = 2n^2 - 7n + 8\), if \(n\) is an integer?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)
Show more


In order to minimize f(n)=2n^2 - 7n + 8, I would need to minimize 2n^2 - 7n as there is nothing I can do about 8, it is just a constant.

In order to minimize 2n^2 - 7n , it has to be less than 0
2n^2 - 7n < 0
Therefore 2n^2 must be less than 7n; which tells me that n has to be greater than 0 and less than 4

As I start picking values for n, I get the following:
For n=1; f(n)= 3
For n=2; f(n)= 2
For n=3 ; f(n)=5

Hence the minimum value of f(n)=2n^2 - 7n + 8 is 2.

Correct answer is B

Bunuel KarishmaB can you please check the reasoning followed above to solve this question and tell me if there are any flaws in it?
Thank you in advance for your feedback.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,959
Own Kudos:
1,117
Posts: 38,959
Kudos: 1,117
What is the minimum value of f(n) = 2n^2 - 7n + 8, if n 07 Aug 2025, 11:06
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
109763 posts
Krunaal
Tuck School Moderator
853 posts