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If x is a positive integer, is x a prime integer?
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25 Jan 2013, 02:43
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If x is a positive integer, is x a prime integer? (1) x+1 is a prime number. (2) x5 is a prime number. Can't figure it out.
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Re: If x is a positive integer, is x a prime integer?
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25 Jan 2013, 03:47
If x is a positive integer, is x a prime integer?(1) x+1 is a prime number. Notice that x cannot be an odd prime, because in this case (odd prime) + 1 = (even number), and the only even prime is 2, but in this case x=1, which is not prime. So, if x=prime, then it must be 2: 2+1=3=prime. Of course, x can be a nonprime, for example 1. Not sufficient. (2) x5 is a prime number. If x=7, then the answer is YES but if x=8, then the answer is NO. Not sufficient. (1)+(2) From (1) we have that if x IS a prime, then it must be 2. But if x=2, them x5=3, which is not a prime. Thus x=prime=2 contradicts the second statement. Therefore x cannot be a prime number. Sufficient. Answer: C. Hope it's clear.
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Re: If x is a positive integer, is x a prime integer?
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20 May 2013, 02:15
suprememodelrus wrote: If x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
Hi Bunuel, My approach does not look standard. Is it correct? From statement 1: X= 1,2,4,6,10,12,16,18........ From statement 2: X= 7,8,10,12,16,22........ common from the both statements are 10,12,16..... Thus X is not a prime integer. Kindly provide algebric approach if possible. Thanks in advance
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Re: If x is a positive integer, is x a prime integer?
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20 May 2013, 08:41
f x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
I think this is a bad question , however ...
from 1
x , x+1 are 2 successive integers ....... if x is prime and since the only 2 prime that are successive are 2,3 therefore if x is prime it is 2 , however x could be 4 as well .... insuff
from 2
The only 2 primes 5 units apart are 7 and 2 , (since all primes > 3 end in 1,3,7,9) if x were to be prime it is 7 , however x could be 8 and (x5) could be 3 ... insuff
both together
for x to be prime according to the above 2 statements then it has be less than a prime by 1 and larger than another by 5 .... there exist no such a prime
thus sure x is not a prime ( integers if not prime are composite)



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Re: If x is a positive integer, is x a prime integer?
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21 May 2013, 00:05
atalpanditgmat wrote: suprememodelrus wrote: If x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
Hi Bunuel, My approach does not look standard. Is it correct? From statement 1: X= 1,2,4,6,10,12,16,18........ From statement 2: X= 7,8,10,12,16,22........ common from the both statements are 0,12,16..... Thus X is not a prime integer. Kindly provide algebric approach if possible. Thanks in advance Yes, that's correct. From both statements x must be even (10, 12, 16, ...), but it cannot be 2. So, x is not a prime number.
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Re: If x is a positive integer, is x a prime integer?
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29 Jan 2014, 07:01
Correct. From both statements together:
X must be higher than 5 because no prime can be negative. All primes higher than 5 are odd. So x+1 will be an even number. There is only one even number that is prime which is 2. Given that x>5 then we know that X cannot be a prime
C



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Re: If x is a positive integer, is x a prime integer?
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29 Aug 2018, 07:57
If x is a positive integer, is x a prime integer? (1) x+1 is a prime number. x+1 can be either of 2,3,5,7,11,13,17,19,... etc Hence, X can be either of 1,2,4,6,10,12,16,18,...etc Here X=2 is prime, while other values are nonprime NOT SUFFICIENT(2) x5 is a prime number. x5 can be either of 2,3,5,7,11,13,17,19,... etc Hence, X can be either of 7,8,10,12,16,18,22,24,...etc Here X=7 is prime, while other values are nonprime NOT SUFFICIENTConsidering (1) and (2) together, X can be 10,12,16,18...etc all of this values are even values greater than 2 hence, X cannot be prime SUFFICIENT
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Re: If x is a positive integer, is x a prime integer?
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30 Aug 2018, 22:53
Statement 1x+1 is prime when x =2, both x+1 and x are prime numbers However when x= 4,6,10…, while x+1 is prime, x is not prime Therefore, Statement 1 is insufficient Statement 2x5 is prime when x= 7 both x5 and x are prime numbers However when x= 8,10,12…, while x5 is prime, x is not Therefore Statement 2 is insufficient Statement 1+2Now for x to be prime it has to be equal to 2,3,5,7,11… coming back to the question: is x a prime integer? if both x+1 and x5 are prime numbers: then x cannot be equal to 2, the only prime number which makes x+1 a prime also x cannot be equal to 7, the only prime number which makes x5 a prime for both statements to be true x has to be a non prime value Hence 1+2 is sufficient




Re: If x is a positive integer, is x a prime integer? &nbs
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30 Aug 2018, 22:53






