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# If n is any prime number greater than 2, which of the following CANNOT

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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03 Jul 2018, 01:49
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55% (hard)

Question Stats:

50% (01:05) correct 50% (01:16) wrong based on 92 sessions

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If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

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If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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Updated on: 03 Jul 2018, 02:52
Bunuel wrote:
If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

Note: n> 2 . all prime.

We have to find out the option that can't be prime.

It's given that m is a prime greater than 2. Some one can scan the answer choices.

**** Option E that us even integer all time for any prime greater than 2. ***** only even that is prime is 2. but it is impossible here.

Originally posted by KSBGC on 03 Jul 2018, 02:00.
Last edited by KSBGC on 03 Jul 2018, 02:52, edited 1 time in total.
Director
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Re: If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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03 Jul 2018, 02:45
Bunuel wrote:
If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

2 is the only even prime number
any number greater than 2 has to be an odd number to be considered as a prime number

if n is prime n-1 will always be even
therefore ,
C can never be a prime number
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If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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Updated on: 03 Jul 2018, 03:05
CounterSniper wrote:
Bunuel wrote:
If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

2 is the only even prime number
any number greater than 2 has to be an odd number to be considered as a prime number

if n is prime n-1 will always be even
therefore ,
C can never be a prime number

what if n = 3

n-1 = 3-1 = 2

question make told us that n> 2. but he doesn't tell us that result must be greater that 2 . thanks.

Originally posted by KSBGC on 03 Jul 2018, 02:51.
Last edited by KSBGC on 03 Jul 2018, 03:05, edited 1 time in total.
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Posts: 737
Concentration: Strategy, General Management
Re: If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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03 Jul 2018, 02:55
selim wrote:
CounterSniper wrote:
Bunuel wrote:
If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

2 is the only even prime number
any number greater than 2 has to be an odd number to be considered as a prime number

if n is prime n-1 will always be even
therefore ,
C can never be a prime number

what if n = 3

n-1 = 3-1 = 2

Should be greater than 2
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Re: If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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03 Jul 2018, 05:58
CounterSniper wrote:
Should be greater than 2

CounterSniper

n has to be greater than 2, but n-1 can be any number (prime). Thus when n=3, n-1=2 - prime. The answer is E
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If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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04 Jul 2018, 04:34
Hero8888 wrote:
CounterSniper wrote:
Should be greater than 2

CounterSniper

n has to be greater than 2, but n-1 can be any number (prime). Thus when n=3, n-1=2 - prime. The answer is E

n > 2 must always be odd
all except E can be prime numbers , as odd+odd=even and even no > 2 can never be prime !!
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Re: If n is any prime number greater than 2, which of the following CANNOT  [#permalink]

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06 Feb 2019, 06:47
Bunuel wrote:
If n is any prime number greater than 2, which of the following CANNOT be a prime number?

A. n-4
B. n-3
C. n-1
D. n+2
E. n+5

The longer way would be to plug in numbers of small primes:
A) 7-4=3, prime
B) 5-3=2, prime
C) 3-1=2, prime
D) 3+2=5, prime

The shorter way: realize that all primes except 2 and 5 end in either 1, 3, 7 or 9. n>2, so if we add 5 to any of those besides 2 we get an even number (e.g. 6, 8, 10, 12, 14).
Re: If n is any prime number greater than 2, which of the following CANNOT   [#permalink] 06 Feb 2019, 06:47
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