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Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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19 Nov 2014, 04:24
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Does P have a factor X where 1 < X < P, and X and P are positive integers? (1) GCD (P^2, k) = k, where k is a prime number (2) 36*20 + 2 < P < 36*20+6
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Last edited by Bunuel on 19 Nov 2014, 04:25, edited 1 time in total.
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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19 Nov 2014, 04:37
Does P have a factor X where 1 < X < P, and X and P are positive integers?The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number). (1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient. (2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient. Answer: B.
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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19 Nov 2014, 04:38
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Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Similar questions to practice: ifxisanintegerdoesxhaveafactornsuchthat100670.htmldoestheintegerkhaveafactorpsuchthat1pk126735.htmlforanyintegerngreaterthan1ndenotestheproductof168575.htmldoesintegernhave2factorsxysuchthat1xyn165983.htmlifzisanintegeriszprime128732.htmlHope this helps.
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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15 Nov 2015, 09:37
Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. but what about X itself. for example, if X=721 and in this case it is not a factor of P?



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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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15 Nov 2015, 22:59
vadam wrote: Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. but what about X itself. for example, if X=721 and in this case it is not a factor of P? Your question is not clear. First of all the question asks "Does P have a factor X where 1 < X < P..." plus, an integer is a factor of itself. For example, 721 is a factor of 721.
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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09 Feb 2016, 18:34
manpreetsingh86 wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers? (1) GCD (P^2, k) = k, where k is a prime number from this, we know that k is a factor of p^2. but we don't know whether k is a factor of P or not. what if k=p? what if k=p=1? p^2=1. since we need integers, there might be no x at all here. suppose we have p=9 k=3. then yes. it might be a number x that is a factor of p. (2) 36*20 + 2 < P < 36*20+6 722 < P < 726 p can be 723, 724, 725. 724 is even, so it is divisible 725 ends in 5 so is divisible by 5 7+2+3=12, so divisible by 3 we see that all possible options of P have other factors. we can give a definite answer. B.



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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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16 Mar 2016, 04:05
Here all the values between 36*20+2 and 36*20+6 are non primes as it it possible to obtain the factors. Hence B is sufficient statement 2 can be discarded as p can be 3 and p can be 81 (for k=3) thus B is sufficient
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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08 Oct 2017, 16:47
Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Hi Bunuel.. How did u conclude that P is a prime number? Pls help..thanks in advance



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Re: Does P have a factor X where 1<X<P , and X and P are positive integers [#permalink]
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08 Oct 2017, 20:01
zanaik89 wrote: Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Hi Bunuel.. How did u conclude that P is a prime number? The question asks whether p is prime. If p is prime it won't have a factor x such that 1 < x < p, if p is NOT prime it will have a factor x such that 1 < x < p. For example, prime number 7, does not have a factor x such that 1 < x < 7. Pls help..thanks in advance Where does it say that p is a prime?
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Re: Does P have a factor X where 1<X<P , and X and P are positive integers
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