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What is the value of a positive integer x? (1) x has exactly two disti
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26 Sep 2018, 04:35
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Re: What is the value of a positive integer x? (1) x has exactly two disti
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26 Sep 2018, 05:44
Bunuel wrote: What is the value of a positive integer x?
(1) x has exactly two distinct factors. (2) The difference between any two distinct factors of x is odd. Question: WHat is the value of Positive integer x?Statement 1: x has exactly two distinct factors.i.e. x is Prime Numberbut x may be 2, 3, 5, 7, 11 etc hence NOT SUFFICIENT Statement 2: The difference between any two distinct factors of x is odd.This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even which is possible only if x is 2 because only 2 has one even and one odd factorAnswer: Option B
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Re: What is the value of a positive integer x? (1) x has exactly two disti
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01 Oct 2018, 04:26
GMATinsight wrote: Bunuel wrote: What is the value of a positive integer x?
(1) x has exactly two distinct factors. (2) The difference between any two distinct factors of x is odd. Question: WHat is the value of Positive integer x?Statement 1: x has exactly two distinct factors.i.e. x is Prime Numberbut x may be 2, 3, 5, 7, 11 etc hence NOT SUFFICIENT Statement 2: The difference between any two distinct factors of x is odd.This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even which is possible only if x is 2 because only 2 has one even and one odd factorAnswer: Option B How can we deduce that the number is prime? It doesn't say that the number has only 2 factors that are distinct. Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd. Please clarify



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Re: What is the value of a positive integer x? (1) x has exactly two disti
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01 Oct 2018, 04:31
RustagiABC wrote: GMATinsight wrote: Bunuel wrote: What is the value of a positive integer x?
(1) x has exactly two distinct factors. (2) The difference between any two distinct factors of x is odd. Question: WHat is the value of Positive integer x?Statement 1: x has exactly two distinct factors.i.e. x is Prime Numberbut x may be 2, 3, 5, 7, 11 etc hence NOT SUFFICIENT Statement 2: The difference between any two distinct factors of x is odd.This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even which is possible only if x is 2 because only 2 has one even and one odd factorAnswer: Option B How can we deduce that the number is prime? It doesn't say that the number has only 2 factors that are distinct. Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd. Please clarify Please read the statement more carefully It explicitly mentions that x has exactly two distinct factorsSo there are only two factors of number that are distinct.
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Re: What is the value of a positive integer x? (1) x has exactly two disti
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01 Oct 2018, 04:34
The second statement says
The difference between any two distinct factors of x is odd.



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What is the value of a positive integer x? (1) x has exactly two disti
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Updated on: 01 Oct 2018, 05:15
RustagiABC wrote: The second statement says
The difference between any two distinct factors of x is odd. RustagiABCSuppose a number has three factors  In that case 1) either two of them will be odd and one will be even OR 2) two will be even and one will be odd OR 3) All will be even OR 4) all will be odd The difference of any two factors in first case or second case can't be ODD cause in first case oddodd will be even and in second case eveneven will be even theerfore for the difference of any two factors of the number to be odd ONE FACTOR MUST BE EVEN and ONE FACTOR MUST BE ODD I hope this explains your doubt now...
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Originally posted by GMATinsight on 01 Oct 2018, 05:12.
Last edited by GMATinsight on 01 Oct 2018, 05:15, edited 1 time in total.



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Re: What is the value of a positive integer x? (1) x has exactly two disti
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01 Oct 2018, 05:14
RustagiABC wrote: GMATinsight wrote: Bunuel wrote: What is the value of a positive integer x?
(1) x has exactly two distinct factors. (2) The difference between any two distinct factors of x is odd. Question: WHat is the value of Positive integer x?Statement 1: x has exactly two distinct factors.i.e. x is Prime Numberbut x may be 2, 3, 5, 7, 11 etc hence NOT SUFFICIENT Statement 2: The difference between any two distinct factors of x is odd.This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even which is possible only if x is 2 because only 2 has one even and one odd factorAnswer: Option B How can we deduce that the number is prime? It doesn't say that the number has only 2 factors that are distinct. Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd. Please clarify Hi You are overlooking the info provided in option B , number 14 has 4 factors such as 1,2,7,14 and the difference between 142=12 which is an even number. You are just taking the pairs but the option says the difference between any two factors is odd. hope its clear now. Anurag Jain I don't mind Kudos



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Re: What is the value of a positive integer x? (1) x has exactly two disti
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01 Oct 2018, 19:45
From statement 1 we get that x has exactly 2 distinct factors = meaning its a prime number. So it could be any prime number. 2,3,5,etc.. So, statement 1 is insufficient. From statement 2 we get that the difference between any two distinct factors of x is odd. That is one of the factors is even and the other odd. Because, if any of the two distinct factors were odd then the difference would be odd odd = even, or if any of two distinct factors were even then also we would have got the difference as even  even = even. So, the only way one can get the difference of the ANY 2 distinct factors odd is even  odd = odd or odd  even = odd. So, only number 2 satisfies this quality. Because it has only 2 factors and ANY 2 factors are those 2 factors, ie 1 and 2. So, 21 = 1 (odd). So, statement 2 itself is sufficient. Corollary: This is a type of question where one may take the help of Statement 1 to get the answer and hence mark the wrong answer C. Since, statement 2 is itself is sufficient. Answer is B.




Re: What is the value of a positive integer x? (1) x has exactly two disti &nbs
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