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ifthyder
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 Posted: Sat Aug 30, 2008 1:27 am Post subject: q#132 OG 11th edition page 331 |
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Q132) if the integer n is greater than 1 is n equal to 2?
1)n has exactly two positive factors.
2)the difference of any two distinct positibe factores of n is odd.
answer is B
explaination
2) note tha if n>2 and n is odd then 1 and n are factors of n , and their difference is even. also if n >2 and n is even,
then 2 and n are factors of n and their difference is even.
Now according to me if we take even value of n >2 for example 6 as n value and take two factors of 6 in such a way that one factor of n be even i.e 2 and other factor of 6 be odd i.e 3 then , difference of factors will be 3-2 =1 (odd).Isn't that answer insufficient
6 could be value of n isn't it? |
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Stuart Kovinsky
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| Posted: Sat Aug 30, 2008 1:50 am Post subject: Re: q#132 OG 11th edition page 331 |
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| ifthyder wrote: | Q132) if the integer n is greater than 1 is n equal to 2?
2)the difference of any two distinct positibe factores of n is odd.
Now according to me if we take even value of n >2 for example 6 as n value and take two factors of 6 in such a way that one factor of n be even i.e 2 and other factor of 6 be odd i.e 3 then , difference of factors will be 3-2 =1 (odd).Isn't that answer insufficient
6 could be value of n isn't it? |
You're misinterpreting statement (2). You need to interpret "any two factors" as "every pair of factors".
So, even though some pairs of factors of 6 have an odd difference, it's not true that every pair of factors of 6 have an odd difference. For example, the difference between 1 and 3 is even.
The only way for the difference between every pair of factors to be odd is if the number has exactly 2 factors: 1 even and 1 odd. Only "2" fits that description, so statement (2) gives us a definite "yes" answer to the question.
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olpre4
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| Posted: Mon Sep 01, 2008 7:39 pm Post subject: What about n = 6? |
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Factors for 6
3x2 --> 3-2 = 1 odd
6x1 --> 6-1 = 5 odd
Could n be 6 as well? |
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olpre4
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| Posted: Mon Sep 01, 2008 7:45 pm Post subject: 3x1 Reply? |
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How is 3x1 a factor pair of 6?
Unless I am thinking about things the wrong way, I can only identify 3x2 and 6x1 as factors of 6. |
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Ian Stewart
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| Posted: Tue Sep 02, 2008 3:17 am Post subject: Re: 3x1 Reply? |
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| olpre4 wrote: | How is 3x1 a factor pair of 6?
Unless I am thinking about things the wrong way, I can only identify 3x2 and 6x1 as factors of 6. |
While you're right that those are the only pairs of positive integers with a product of six, the question does not mention 'factor pairs'. Factors are divisors. The positive factors of 6 are 1, 2, 3 and 6. |
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