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For how many positive integers n is n^2 - 3n + 2 a prime number?

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Math Expert
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For how many positive integers n is n^2 - 3n + 2 a prime number?  [#permalink]

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New post 19 Mar 2019, 00:04
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:31) correct 41% (01:38) wrong based on 98 sessions

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Re: For how many positive integers n is n^2 - 3n + 2 a prime number?  [#permalink]

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New post 19 Mar 2019, 01:28
2

Solution


Given:
    • The number n is a positive integer
    • The expression \(n^2 – 3n + 2\) is a prime number

To find:
    • The number of values possible for n

Approach and Working:
If n = even,
    • then \(n^2 – 3n + 2\) = even – even + even = even

if n = odd,
    • then \(n^2 – 3n + 2\) = odd – odd + even = even

Hence, for any value of n, the expression results in an even prime number.

We also know that 2 is the only even prime number.
    • Therefore, \(n^2 – 3n + 2 = 2\)
    Or, \(n^2 – 3n = 0\)
    Or, \(n = 3\) (as n cannot be 0)

Hence, the correct answer is option B.

Answer: B

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Re: For how many positive integers n is n^2 - 3n + 2 a prime number?  [#permalink]

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New post 19 Mar 2019, 03:54
1
Bunuel wrote:
For how many positive integers n is n^2 - 3n + 2 a prime number?


(A) none
(B) one
(C) two
(D) more than two, but finitely many
(E) infinitely many


we can reqrite given expression as
n^2 - 3n + 2
n(n-2)-1(n-2)
n=2,1
prime no 2 only 1
IMO B
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For how many positive integers n is n^2 - 3n + 2 a prime number?  [#permalink]

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New post 21 May 2019, 04:25
Archit3110 wrote:
Bunuel wrote:
For how many positive integers n is n^2 - 3n + 2 a prime number?


(A) none
(B) one
(C) two
(D) more than two, but finitely many
(E) infinitely many


we can reqrite given expression as
n^2 - 3n + 2
n(n-2)-1(n-2)
n=2,1
prime no 2 only 1
IMO B

But where does it say that the given exp. is equal to zero ? The exp. can at max.be reduced to (n-2)(n-1), this does not necessarily mean that n =2 or n=1 , the variable n can take an infinite number of values. Unless and until we know the RHS of the exp. we cannot deduce the value of n. Hope you agree.

The method given above by EgmatQuantExpert uses a better logic,I suppose.

Again let me know if I have missed anything. Thanks.
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For how many positive integers n is n^2 - 3n + 2 a prime number?   [#permalink] 21 May 2019, 04:25
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