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Bunuel
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.
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Bunuel
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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CounterSniper

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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Hero8888
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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


My Bad !! should read the question more carefully !!
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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Bunuel
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
E) only answer left

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).
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A) 7-4=3 ok
B) 5-3=2 ok
C) 3-1=2 ok
D) 3+2=5 ok
E) Our answer
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