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Can the positive integer p be expressed as the product of [#permalink]
 27 Dec 2009, 05:49
Question Stats:
73% (01:32) correct
26% (00:29) wrong based on 8 sessions
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? 1) 31 < p < 37 2) p is odd
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Re: Positive integer problem [#permalink]
27 Dec 2009, 07:24
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Minotaur wrote: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1 ? (1) 31 < p < 37 (2) p is odd OA: can anyone help me with the explanation to this problem. The wording makes this question harder than it is actually. If positive integer p cannot be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? (1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient. (2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient. Answer: A.
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Re: Positive integer problem [#permalink]
27 Dec 2009, 08:27
s1)----> p can be 32,33,34,35,36 each no. is having at least 2 factors >1 hence yes .....therfore suff s2)----> p can be any odd int and for odd like 3 , 5,7 ans is no and for no's such as 15,21,27, ans is yes hence insuff
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Re: Positive integer problem [#permalink]
17 Jun 2010, 07:45
Thanks for the explanation Buunel and xcusemeplz2009.
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Re: Positive integer problem [#permalink]
08 Jul 2011, 20:51
1. Sufficient
p can be 32 or 33 or 34 or 35 or 36
and each of these numbers can be expressed as product of two integers that are >1 . (32 = 2*16 , 33 = 3*11....)
2. Not sufficient
p is odd
p = 1 3 5 15
when p= 1 or 3 or 5 it cannot be expressed as product of two integers greater than 1. (as 5 = 1*5)
when p=15 , p can be expressed as product of two integers greater than 1.
Answer is A.
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Re: Positive integer problem [#permalink]
25 Aug 2011, 13:38
Bunuel,
This question confuses me big time. When I saw "CAN" I expected as sufficient to be able to prove that yes, there was a way to do so. Hence for statement (2) I'd say that yes, IT CAN BE EXPRESSED AS THE PRODUCT OF TWO INTEGERS. Do you consider the following two statements to have the same meaning?
(i) Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
(ii) Is the positive integer p the product of two integers, each of which is greater than 1?
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Re: Positive integer problem [#permalink]
16 Sep 2011, 10:16
Bunuel wrote: Minotaur wrote: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1 ? (1) 31 < p < 37 (2) p is odd OA: can anyone help me with the explanation to this problem. The wording makes this question harder than it is actually. If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? (1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient. (2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient. Answer: A. If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? how can u say this..please elaborate...how p is prime...any no greater than one can be any no..why r u sayin p is prime?
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Re: Positive integer problem [#permalink]
16 Sep 2011, 11:26
ruturaj wrote: If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime?
how can u say this..please elaborate...how p is prime...any no greater than one can be any no..why r u sayin p is prime? Prime number can only be expressed as "1*p", where p is the prime number itself 13=1*13 Can we write any prime number in the form; p=m*n where, p=prime number m=integer greater than 1 n=integer greater than 1 No, right? For prime number, at least one of m and n must be 1. Thus, question is indirectly asking whether p is a prime number.
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Re: Can the positive integer p be expressed as the product of [#permalink]
23 Feb 2012, 21:08
I don't understand this question. I am getting E. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? Statement (1) states that 31<p<37 My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = -9 x -4 and each integer is not greater than 1, so insufficient. Statement (2), I agree it is insufficient. (1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be -7x-5 so each integer is not greater than 1. Am I misunderstanding the question?
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Re: Can the positive integer p be expressed as the product of [#permalink]
24 Feb 2012, 01:25
chamisool wrote: I don't understand this question. I am getting E. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? Statement (1) states that 31<p<37 My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = -9 x -4 and each integer is not greater than 1, so insufficient. Statement (2), I agree it is insufficient. (1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be -7x-5 so each integer is not greater than 1. Am I misunderstanding the question? It seems that you misinterpreted the question. Look at the definition of a prime number: a prime number is a positive integer with exactly two factors: 1 and itself. Now, the questions asks: "can the positive integer p be expressed as the product of two integers, each of which is greater than 1" So, the question basically asks whether p is a prime number, because if it is then p can NOT be expressed as the product of two integers, each of which is greater than 1. (1) states: 31 < p < 37. Between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers, which means that the answer to the question is YES: p can always be expressed as the product of two integers, each of which is greater than 1. Sufficient. Just to illustrate: 32=2*18, 33=3*11, 34=2*17, 35=5*7, 36=2*18. Hope it's clear.
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Can the positive integer P be expressed as a product of 2... [#permalink]
28 Feb 2012, 15:28
Can the positive integer P be expressed as a product of two integers,each of which is greater than 1? (1) 31<p<37 (2) p=odd The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1? Thank you in advance
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Re: Can the positive integer P be expressed as a product of 2... [#permalink]
28 Feb 2012, 15:35
Merging similar topics. vladkarz wrote: Can the positive integer P be expressed as a product of two integers, each of which is greater than 1? (1) 31<p<37 (2) p=odd The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1? Thank you in advance P is some particular integer and we are asked whether it can be expressed as a product of two integers, each of which is greater than 1. Now, for (2) if p=9 then the answer is YES, it can be expressed as a product of two integers, each of which is greater than 1 but of p=5 then the answer is NO, it cannot be expressed as a product of two integers, each of which is greater than 1. Two different answers, hence this statement is not sufficient. Does it makes sense? P.S. Please refer for a complete solution to the above posta and ask if anything remains unclear.
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Re: Can the positive integer P be expressed as a product of 2... [#permalink]
28 Feb 2012, 16:51
Bunuel wrote: Merging similar topics. vladkarz wrote: Can the positive integer P be expressed as a product of two integers, each of which is greater than 1? (1) 31<p<37 (2) p=odd The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1? Thank you in advance P is some particular integer and we are asked whether it can be expressed as a product of two integers, each of which is greater than 1. Now, for (2) if p=9 then the answer is YES, it can be expressed as a product of two integers, each of which is greater than 1 but of p=5 then the answer is NO, it cannot be expressed as a product of two integers, each of which is greater than 1. Two different answers, hence this statement is not sufficient. Does it makes sense? P.S. Please refer for a complete solution to the above posta and ask if anything remains unclear. Thank you very much Bunuel, So basically if there are 2 possible answers (yes/no) it will always be insufficient?
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Re: Can the positive integer P be expressed as a product of 2... [#permalink]
28 Feb 2012, 16:55
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Re: Can the positive integer p be expressed as the product of [#permalink]
08 Apr 2012, 05:51
Bunuel wrote: chamisool wrote: I don't understand this question. I am getting E. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? Statement (1) states that 31<p<37 My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = -9 x -4 and each integer is not greater than 1, so insufficient. Statement (2), I agree it is insufficient. (1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be -7x-5 so each integer is not greater than 1. Am I misunderstanding the question? It seems that you misinterpreted the question. Look at the definition of a prime number: a prime number is a positive integer with exactly two factors: 1 and itself. Now, the questions asks: "can the positive integer p be expressed as the product of two integers, each of which is greater than 1" So, the question basically asks whether p is a prime number, because if it is then p can NOT be expressed as the product of two integers, each of which is greater than 1. (1) states: 31 < p < 37. Between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers, which means that the answer to the question is YES: p can always be expressed as the product of two integers, each of which is greater than 1. Sufficient. Just to illustrate: 32=2*18, 33=3*11, 34=2*17, 35=5*7, 36=2*18. Hope it's clear. I think as you said, the key to this problem are the words each of which is greater than one
is correct ??? You think the problem can be solved even if you do not see this nuance ?? thanks
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Re: Can the positive integer p be expressed as the product of [#permalink]
13 Apr 2013, 08:13
Ah...I struggled with this one at first as well
I originally got D because I thought the question was asking if we can have product of two numbers for p.
Key for me was reminding myself that this is as "Yes or No" question, which means that it's "always yes" or "always no." For some reason, I had interpreted "Can the positive..." as is there a single instance where it can be true.
1) 31 < p < 37...
32 = 8 x 4
33 = 11 x 3
34 = 2 x 17
35 = 5 x7
36= 6 x 6
sufficient
2) p is odd
p = 5
p = 15
not sufficient
So, the answer is A because statement 2 is not ALWAYS sufficient
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Re: Can the positive integer p be expressed as the product of
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13 Apr 2013, 08:13
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