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Bunuel
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n Mar 28, 2023 12:45 pm
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69% (01:52) correct 31% (01:46) wrong based on 589 sessions

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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. \(5\)
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B
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n May 03, 2023 9:48 am
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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
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)
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n Updated on: Feb 22, 2025 8:14 am
Originally posted by GMATinsight on Mar 28, 2023 1:07 pm.
Last edited by Bunuel on Feb 22, 2025 8:14 am, edited 3 times in total.
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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
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n Mar 28, 2023 1:43 pm
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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
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The result of the highlighted part must be 2. So, the correct answer must be B.
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n May 02, 2023 8:14 pm
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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.
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What is the minimum value of f(n) = 2n^2 - 7n + 8, if n Aug 07, 2025 6:06 pm
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