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If n is a prime number greater than 65, then which of the following

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If n is a prime number greater than 65, then which of the following  [#permalink]

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New post 24 Mar 2019, 00:23
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Question Stats:

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If n is a prime number greater than 65, then which of the following statements must be true?

I. 2n + 1 leaves a remainder of 3 when divided by 4
II. (n-1)(n+7) is divisible by 12
III. (n^2-1)^2 is divisible by 72

A. I and II only
B. I and III only
C. II and III only
D. I, II and III
E. None out of I, II and III
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Re: If n is a prime number greater than 65, then which of the following  [#permalink]

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New post 24 Mar 2019, 20:29
Is the OA correct?.. Explanations please.


kiran120680 wrote:
If n is a prime number greater than 65, then which of the following statements must be true?

I. 2n + 1 leaves a remainder of 3 when divided by 4
II. (n-1)(n+7) is divisible by 12
III. (n^2-1)^2 is divisible by 72

A. I and II only
B. I and III only
C. II and III only
D. I, II and III
E. None out of I, II and III
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Re: If n is a prime number greater than 65, then which of the following  [#permalink]

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New post 24 Mar 2019, 20:45
kiran120680 wrote:
If n is a prime number greater than 65, then which of the following statements must be true?

I. 2n + 1 leaves a remainder of 3 when divided by 4
II. (n-1)(n+7) is divisible by 12
III. (n^2-1)^2 is divisible by 72

A. I and II only
B. I and III only
C. II and III only
D. I, II and III
E. None out of I, II and III


test with values of n =67 & 71
2n + 1 leaves a remainder of 3 when divided by 4 ; sufficient
(n-1)(n+7) is divisible by 12; sufficient
(n^2-1)^2 is divisible by 72; ( 71^2-1)^2 ; ((71+1)*(71-1) )^2 ; ( ((72)*(70)^2 ; divisible by 72 ; sufficient
IMO D
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Re: If n is a prime number greater than 65, then which of the following   [#permalink] 24 Mar 2019, 20:45
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If n is a prime number greater than 65, then which of the following

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