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When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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09 Apr 2015, 07:31
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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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09 Apr 2015, 10:24
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Bunuel wrote: When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
Kudos for a correct solution. Statement A states that when 900 is divided by d, remainder r = 1. This doesn't give any info about R or D; InsufficientStatement B states that when N is divided by D = 23, remainder R = x. This doesn't give any info about r or d; InsufficientCombining A and B; Since 900/d give r=1 => d is a factor of 899 The tricky part : factors of 899 = 29*31 (took me a while to figure this out, started with the approx values around 30 as it is close to 900) this means d could be either 29 or 31 From B, D=23 and R being the reminder can't be greater than 23 => R < 23 Since d could be either 29 or 31, which both are greater than 23 and in turn R. Hence, SufficientAnswer C



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When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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09 Apr 2015, 23:46
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Bunuel wrote: When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
Kudos for a correct solution. (1) r = 1 Insufficient as no information about R. (2) D = 23 Insufficient as no information about d. Together :N= 23*M + R , R<23 900 = d*K + 1 , d can be 899 or 29, 31 . as \(899=(9001)=(30^2 1^2) = 29*31\) . for all possible values of d, R<d . Answer C
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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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13 Apr 2015, 05:41
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Bunuel wrote: When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:This is a tricky one about remainders remainders. Statement #1: If r = 1, then we divide 900 by d, and the remainder is 1. This means that d is a factor of 899. That’s interesting, but at the moment, we know zilch about R, which could be anything. This statement, alone and by itself, is not sufficient. Statement #2: If D = 23, then when we divide by 23, the remainder has to be smaller than the divisor. We know R < 23. But, now, the only thing we know about d is that it’s not a factor of 900: d could be 7 or 97. We have no idea of its size, so we can’t compare it to R. This statement, alone and by itself, is not sufficient. Combined:From the second statement, we know R < 23. From the first, we know d must be a factor of 899. What are the factors of 899? For this we will use an advanced factoring technique. Notice that 899 = 900 – 1. This means, we can express 899 as the Difference of Two Squares, because 900 is 30 squared. We can use that algebraic pattern to factors numbers. 899 = 900  1 = 30^2  1^1 = (30 + 1)(30  1) = 31*29. So, it turns out that 899 is the product of two prime numbers, 29 and 31. This means that 899 has four factors: {1, 29, 31, and 899}. Those are the candidate values for d. Obviously, d cannot equal 1, because when we divide any integer by 1, we never get a remainder of any sort: 1 goes evenly into every integer. That means, d could be 29 or 31 or 899. Well, if R < 23, this means that R must be less than d. We can give a definitive “yes” answer to the prompt question. Combined, the statements are sufficient. Answer = (C)
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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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02 Jul 2016, 15:04
King407 wrote: The tricky part : factors of 899 = 29*31 (took me a while to figure this out, started with the approx values around 30 as it is close to 900) this means d could be either 29 or 31
It can be useful to remember that a^2  b^2 = (a+b)(ab). Whenever you see a number that is close to a perfect square, like 899, think of it as (301)(30+1)



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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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03 Jul 2016, 05:43
Bunuel wrote: Bunuel wrote: When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
Kudos for a correct solution. Statement #2: If D = 23, then when we divide by 23, the remainder has to be smaller than the divisor. We know R < 23. But, now, the only thing we know about d is that it’s not a factor of 900: d could be 7 or 97. We have no idea of its size, so we can’t compare it to R. This statement, alone and by itself, is not sufficient. Hi, Statement 2 does not state anything regarding "r" and we know remainder can be greater than or equal to zero i.e r>=o So, if we assume r = 0 then "d" can also be a factor of 900. Am I wrong?



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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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22 Jul 2016, 03:04
subhamgarg91 wrote: Bunuel wrote: Bunuel wrote: When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
Kudos for a correct solution. Statement #2: If D = 23, then when we divide by 23, the remainder has to be smaller than the divisor. We know R < 23. But, now, the only thing we know about d is that it’s not a factor of 900: d could be 7 or 97. We have no idea of its size, so we can’t compare it to R. This statement, alone and by itself, is not sufficient. Hi, Statement 2 does not state anything regarding "r" and we know remainder can be greater than or equal to zero i.e r>=o So, if we assume r = 0 then "d" can also be a factor of 900. Am I wrong? If I got what you're saying you're not wrong, but it wouldn't make statement 2 sufficient either.



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Re: When 900 is divided by positive integer d, the remainder is r. For so [#permalink]
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Re: When 900 is divided by positive integer d, the remainder is r. For so
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