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If x is a positive integer, is x1 a factor of 104? [#permalink]
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22 Jan 2012, 16:44
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If x is a positive integer, is x – 1 a factor of 104? (1) x is divisible by 3. (2) 27 is divisible by x.
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Re: Factor of 104 [#permalink]
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22 Jan 2012, 16:59
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enigma123 wrote: If x is a positive integer, is x – 1 a factor of 104? (1) x is divisible by 3. (2) 27 is divisible by x.
For me the answer is clearly B. But OA is C. Can someone please explain? If x is a positive integer, is x – 1 a factor of 104?(1) x is divisible by 3 > well, this one is clearly insufficient, as x can be 3, x1=2 and the answer would be YES but if x is 3,000 then the answer would be NO. (2) 27 is divisible by x > factors of 27 are: 1, 3, 9, and 27. Now, if x is 3, 9, or 27 then the answer would be YES (as 2, 8, and 26 are factors of 104) BUT if x=1 then x1=0 and zero is not a factor of ANY integer (zero is a multiple of every integer except zero itself and factor of none of the integer). Not sufficient. (1)+(2) As from (1) x is a multiple of 3 then taking into account (2) it can only be 3, 9, or 27. For all these values x1 is a factor of 104. Sufficient. Answer: C.
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Re: If x is a positive integer, is x1 a factor of 104? [#permalink]
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22 Jan 2012, 17:08
Thanks very much buddy for shedding light on concept of ZERO.
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If x is a positive integer, is x1 a factor of 104? [#permalink]
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22 Apr 2015, 23:12
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Hi Guys, The question deals with the concepts of factors and multiples of a number. Its important to analyze the information given in the question first before preceding to the statements. Please find below the detailed solution: StepI: Understanding the QuestionThe question tells us that \(x\) is a positive integer and asks us to find if \(x1\) is a factor of 104 StepII: Draw Inferences from the question statementSince \(x\) is a +ve integer, we can write \(x>0\). The question talks about the factors of 104. Let's list out the factors of 104. \(104 = 13 * 2^3\). So, factors of 104 are {1,2,4,8,13,26,52,104}, a total of 8 factors. If \(x1\) is to be a factor of 104, \(2<=x<=105\). With these constraints in mind lets move ahead to the analysis of the statements. StepIII: Analyze StatementI independentlyStI tells us that \(x\) is divisible by 3. This would mean that \(x\) can take a value of any multiple of 3. Now, all the multiples of 3 are not factors of 104. So, we can't say for sure if \(x1\) is a factor of 104. Hence, statementI alone is not sufficient to answer the question. StepIV: Analyze StatementII independentlyStII tells us that 27 is divisible by \(x\) i.e. \(x\) is a factor of 27. Let's list out the factors of 27  {1,3,9,27}. But, we know that for \(x1\) to be a factor of 104, \(2<=x<=105\). We see from the values of factors of 27, \(x\) can either be less than 2(i.e. 1) or greater than 2 (i.e. 3,9 & 27). Hence, statementII alone is not sufficient to answer the question. StepV: Analyze both statements togetherStI tells us that \(x\) is a multiple of 3 and StII tells us that \(x\) can take a value of {1, 3, 9, 27}. Combining these 2 statements we can eliminate \(x=1\) from the values which \(x\) can take. So, \(x\)={ 3, 9, 27} and \(x1\) = {2, 8, 26}. We observe that all the values which \(x1\) can take is a factor of 104. Hence, combining stI & II is sufficient to answer our question. Answer: Option CTakeawayAnalyze the information given in the question statement properly before proceeding for analysis of the statements. Had we not put constraints on the values of x, we would not have been able to eliminate x=1 from stII analysis. Hope it helps! Regards Harsh
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If x is a positive integer, is x1 a factor of 104? [#permalink]
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20 Sep 2016, 10:28
Let's take x=30, in this case, 1. A Will be sufficient. However 301 is 29 is not a factor of 104. 2. 27 is also not divisible by 30. Not sufficient.
Hence, In this case is the answer E. Can anybody answer my doubt.



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If x is a positive integer, is x1 a factor of 104? [#permalink]
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21 Sep 2016, 01:47
prashantrchawla wrote: Let's take x=30, in this case, 1. A Will be sufficient. However 301 is 29 is not a factor of 104. 2. 27 is also not divisible by 30. Not sufficient.
Hence, In this case is the answer E. Can anybody answer my doubt. I am not sure what you are trying to do here. for statement 1 : you are considering only one value of x, which is making your case sufficient. Take x =3 and x = 6, you will get 104 divisible for x1 = 2 but not for x1 = 5. Hence, it is Insufficient. Statement 2 : We are given 27 is divisible by x. It means x is a factor of 27. The factors could be 1,3,9 and 27. Divide 104 by each of (x1) as 0, 2,8 and 26. You will find 104 divisible by all but 0. hence, insufficient. On combining, we know that x cannot be 0. Hence, Answer C.
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Re: If x is a positive integer, is x1 a factor of 104? [#permalink]
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21 Sep 2016, 03:13



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Re: If x is a positive integer, is x1 a factor of 104? [#permalink]
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04 Dec 2017, 11:54
enigma123 wrote: If x is a positive integer, is x – 1 a factor of 104?
(1) x is divisible by 3. (2) 27 is divisible by x. Lets look at the prime factorisation of 104: 2^3 * 13 Thus factors of 104 = 1, 2, 4, 8, 13, 26, 52, 104 We are asked whether x1 is one of these 8 integers, OR IS x one of these: 2, 3, 5, 9, 14, 27, 53, 105 (1) x is divisible by 3, so x could be any multiple of 3 like 9 or 27 or 54. Insufficient. (2) 27 is divisible by x, so x is a factor of 27. Now factors of 27 are: 1, 3, 9, 27. If x is 1, then x1 is 0 and thus NOT a factor of 104, but if x is 3 or 9 or 27, then x1 will take values as 2 or 8 or 26 respectively, and thus BE a factor of 104. So Insufficient. Combining the two statements, x has to be a multiple of 3, yet a factor of 27 also. So x could be either 3 or 9 or 27. For each of these cases, x1 will be a factor of 104, as explained in statement 2. Sufficient. Hence C answer




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