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

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Director
Joined: 18 Feb 2019
Posts: 603
Location: India
GMAT 1: 460 Q42 V13
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If n is a prime number greater than 65, then which of the following  [#permalink]

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24 Mar 2019, 00:23
00:00

Difficulty:

85% (hard)

Question Stats:

40% (02:26) correct 60% (02:33) wrong based on 30 sessions

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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
Manager
Joined: 31 Oct 2018
Posts: 77
Location: India
Re: If n is a prime number greater than 65, then which of the following  [#permalink]

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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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Joined: 18 Aug 2017
Posts: 5436
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If n is a prime number greater than 65, then which of the following  [#permalink]

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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
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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