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If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 02:13
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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 04:39
St1: x does not have a factor p such that 2<p<x. Case 1: x is not prime. Say x = 10. p could be 5 and the condition 2<5<10 will hold true. But we want that this condition should not happen. x cannot be prime. Case 2: x is prime. Since prime number only has the number and 1 as its factors, it will never have any factor p such that 2<p<x. x is definitely prime excluding 2 and 3. Sufficient. St2: The product of any two factors of x is greater than 2 but less than 10. If x is any of 3, 5 or 7 (primes)  the product will be less than 10. If x is 9 (non prime)  the product will be less than 10. Not sufficient. Answer (A). I hope I'm right.



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 05:53
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Donnie84 wrote: St1: x does not have a factor p such that 2<p<x. Case 1: x is not prime. Say x = 10. p could be 5 and the condition 2<5<10 will hold true. But we want that this condition should not happen. x cannot be prime. Case 2: x is prime. Since prime number only has the number and 1 as its factors, it will never have any factor p such that 2<p<x. x is definitely prime excluding 2 and 3. Sufficient. St2: The product of any two factors of x is greater than 2 but less than 10. If x is any of 3, 5 or 7 (primes)  the product will be less than 10. If x is 9 (non prime)  the product will be less than 10. Not sufficient. Answer (A). I hope I'm right. Statement 1. What if x = 4 (not prime)? It has factors: 1, 2 and 4. All these factors satisfy inequality 2<p<x. INSUFFICIENT. Statement 2. If x is 9, then 3*9 = 27 but the statement says that the product of ANY two factors of x is less than 10. So, there are only 3, 5 and 7 that satisfy to restriction. SUFFICIENT. IMO correct answer is B.



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 06:19
magneticlp wrote: Donnie84 wrote: St1: x does not have a factor p such that 2<p<x. Case 1: x is not prime. Say x = 10. p could be 5 and the condition 2<5<10 will hold true. But we want that this condition should not happen. x cannot be prime. Case 2: x is prime. Since prime number only has the number and 1 as its factors, it will never have any factor p such that 2<p<x. x is definitely prime excluding 2 and 3. Sufficient. St2: The product of any two factors of x is greater than 2 but less than 10. If x is any of 3, 5 or 7 (primes)  the product will be less than 10. If x is 9 (non prime)  the product will be less than 10. Not sufficient. Answer (A). I hope I'm right. Statement 1. What if x = 4 (not prime)? It has factors: 1, 2 and 4. All these factors satisfy inequality 2<p<x. INSUFFICIENT. Statement 2. If x is 9, then 3*9 = 27 but the statement says that the product of ANY two factors of x is less than 10. So, there are only 3, 5 and 7 that satisfy to restriction. SUFFICIENT. IMO correct answer is B. Thanks magneticlp. Your solution is indeed correct. I need to be more careful



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 13:55
Statement 1: x does not have a factor p such that 2<p<x.
lets say x=10, then x has 1,2,5,10 as its factors but as per the statement 1, x does not have a factor p such that 2<p<x. hence x cannot be 10. Let say x=7 then x has 1 and 7 as its factors and it completely satisfy the condition 1, hence x can assume 7 as a value.
Moreover we know that prime nos. are divisible by 1 and the number itself, hence only numbers which are going to satisfy the condition mentioned in statement 1 will be prime nos. hence statement 1 sufficient.
Statement 2: The product of any two factors of x is greater than 2 but less than 10 lets say x= 4, then x has 1,2,4 as factors. Now the product of 2 and 4 is greater than 2 and less than 10 hence satisfied the condition. but the product of 1 and 2 doesn't hence x cannot be equal to 4. similar result holds true for all the nonprime numbers hence x cannot be a nonprime number.
lets say x=7 then x has 1,7 as its factors. product of 1 and 7 is greater than 2 and less than 7 hence holds true. Also , the same result holds true for the prime numbers greater than 2 but less than 10. hence x will be a prime number greater than 2 and less than 10. Therefore 2 alone is also sufficient to answer the question.
Hence i will go with option D. Each alone is sufficient to answer the question.



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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14 Feb 2014, 17:30
1) x = 4 works and so does x = 5. One is prime, one is not. Thus, Ins 2) x = 4 (product of 2*4 = 8) and x = 5 (5*1 = 5). Ins. (1+2) Can use the same numbers as above. Ins.
(E) is answer.



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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15 Feb 2014, 00:49
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Quote: If x is a positive integer greater than 1, is x a prime number?[
(1) x does not have a factor p such that 2<p<x.
(2) The product of any two factors of x is greater than 2 but less than 10. 1) 4 and 11 both fulfill the criteria and one is prime the other is not. So 1) alone is insufficient to answer the question 2) 1 and x itself are both factors of x so we know that 2 < x < 10. Can a non prime numbers fulfill the condition ? You just have to try all the nonprime (4,6,8,9), for 4,6 and 8 the factor 2 multiplied by 1 is not greater than 2 and for 9 the factor 3 multiplied by 9 is greater than 10. Conclusion => x has to be prime and 2 is sufficient. Answer is B
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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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15 Feb 2014, 02:07
The correct anser IMO is E
From Statement 1: If x is prime it is true that the factors of are p, such that 2<p<x . But if x=4 (the only case with nonprime), then also the statement holds good.
From Statement 2: Product of any to factors of x are such that 2<product<10. Now this means the number itself has to be less than 10 (or else x*1=x>10, statement doesn't hold). Similarly x*(any other factor, p)<10. That would reduce our choice to nos<=5. But again, we cannot say whether it'll be prime or not (3,4,5 all falls in this category)
I hope its clear.
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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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15 Feb 2014, 06:43



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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16 Feb 2014, 11:26
Bunuel wrote: SOLUTION
If x is a positive integer greater than 1, is x a prime number?
(1) x does not have a factor p such that 2<p<x. Notice that all odd primes satisfy this statement as well as integer 4 (4 does not have a factor p such that 2<p<4). Not sufficient.
(2) The product of any two factors of x is greater than 2 but less than 10. This implies that x can be 3, 5, or 7. Sufficient.
Notice that x cannot be an even number because any even number has 1 and 2 as its factors and the product of these factors is 2, not greater than 2 as given in the statement. Also notice that x cannot be 9 because 3 and 9 both are factors of 9 and 3*9=27>10.
Answer: B. Thanks a lot Bunnel. I had by mistake taken the conditions as >=2 instead of >2 for statement 2 it seems. Thanks a lot again for posting the correct answer



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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27 Mar 2014, 17:18
hi bunnel,
In statement 2: why the case of 4 not considered as the factor of 4 are 4,2,1 & product 4&2 is 8 which is greater than 2 but less than 10 so therefore 4 is also satisying the condition along with 3 , 5, 7 finally we can conclude that staement 2 is insuficent.
Therefore the answer should be B



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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28 Mar 2014, 01:40



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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28 Mar 2014, 01:53
Bunuel wrote: If x is a positive integer greater than 1, is x a prime number?[
(1) x does not have a factor p such that 2<p<x.
(2) The product of any two factors of x is greater than 2 but less than 10. Statement I is insufficient: x = 4  the factors are 1, 2 and 4. So there is no factor which is between 2 and 4. Hence its a NO. x = 3  the factors are 1 and 2. So there is no factor which is between 2 and 4. Hence its a YES (x is a prime number) Statement II is sufficient: Since 1 is a factor of all the numbers hence 2 cannot be a factor of that number. Hence the numbers will have to be either 3, 5 or 7. So Answer is B
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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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28 Mar 2014, 04:53
Hi bunnel Still not clear why are you not considering the case 4*2 =8 where 2. & 4 both are factor of 4



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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28 Mar 2014, 05:00



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Re: If x is a positive integer greater than 1, is x a prime numb [#permalink]
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28 Mar 2014, 08:16
Good question.Got confused in the second statement's use of ANY 2 factors.Couldn't see that even nos. are excluded from this statement very subtly.
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If x is a positive integer greater than 1, is x a prime numb [#permalink]
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19 Nov 2017, 13:39
Answer should be B
Statement 1: no factors of x, such that 2 < p < x => no prime numbers will have factors such that 2<p<x => Also if x = 4, then also no factors between 2<p<4
Not Sufficient
Statement 2: The product of any two factors of x is greater than 2 but less than 10.
Note: For any even number, we ll have (1,2 ) as factors, product of these factors is 2, but given product of any two factors of x is > 2 => x is not even number.
now we are left with {3,5,7,9} => Note, we have cannot have odd numbers greater than 9, if were, then prod of two factors will be greater than 10.
if x were 9, prod of factor (3,9) > 10, so 9 is Out. we are left with {3,5,7} => Prime numbers => Sufficient




If x is a positive integer greater than 1, is x a prime numb
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