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Re: How many positive integers less than 100 have a remainder of
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21 Sep 2009, 20:42
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\(\frac{X2}{13} = n\) where n is a nonnegative integer, and X is a positive integer less than 100. Basically determine how big the subset for possible values of n, and you have your answer. Rearrange the above equation to: 13n + 2 = X and since X < 100, 13n + 2 < 100 13n < 98 n < 98/13 Since n must be an integer.... n < 8 So there are 8 possible values for n (0 to 7), and therefore 8 positive integers less than 100 that have a remainder of 2 when divided by 13. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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Re: How many positive integers less than 100 have a remainder of
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21 Sep 2009, 21:42
My working was like AKProdigy87's Except that 0 is not considered positive (or negative) so the answer should be 7.



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Re: How many positive integers less than 100 have a remainder of
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21 Sep 2009, 23:41
[quote="pejmanjohn"]How many positive integers less than 100 have a remainder of 2 when divided by 13? Easy one. Number closest to 100 but less than 100 and divisible by 13 = 91. 91 = 13 * 7. 91+2 < 100. Satisfies all the conditions. Ans : 7. What is the OA?
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Re: How many positive integers less than 100 have a remainder of
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22 Sep 2009, 11:47
I say 8
13n + 2 < 100
There are 7 possibilities that fit this, but that was not counting 2 (2 / 13 = 0 remainder 2)
So you have 8 positive integers with remainder 2 when divided by 13.... 2, 15, 28, 41, 54, 67, 80, 93



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Re: How many positive integers less than 100 have a remainder of
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22 Sep 2009, 12:36
7
0 divided by anything is a 0  not counted 1st to count is 15
We get 15+13x<100 13x<85 x<6
Plus 15 => 7 integers



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Re: How many positive integers less than 100 have a remainder of
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22 Sep 2009, 17:20
Actually 8 might be the right answer because the question stem is asking what are “the positive integers with a remainder”. This could be interpreted as referring to the dividend, in this case 2 is a valid dividend as 2/13 = 0r2. If this is the case the answer is 8. What is the OA?



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Re: How many positive integers less than 100 have a remainder of
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24 Sep 2009, 10:54
How many positive integers less than 100 have a remainder of 2 when divided by 13?
Simple question. Let the number be A A = 13 * q + 2 here q can take values 0,1,...
since A has to be a two digit number, thus the max value of q that satisfies this condition is q = 7 A = 13 * 7 + 2 = 93
Thus the number of positive integers is from 0 through to 7 inclusive total of 8 numbers



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Re: How many positive integers less than 100 have a remainder of
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21 Oct 2009, 20:26
0 is even number but is not a positive or negative number, so the sol should be 7



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Re: How many positive integers less than 100 have a remainder of
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21 Oct 2009, 21:50
AKProdigy87 wrote: \(\frac{X2}{13} = n\) where n is a nonnegative integer, and X is a positive integer less than 100. Basically determine how big the subset for possible values of n, and you have your answer.
Rearrange the above equation to:
13n + 2 = X
and since X < 100,
13n + 2 < 100 13n < 98 n < 98/13
Since n must be an integer....
n < 8
So there are 8 possible values for n (0 to 7), and therefore 8 positive integers less than 100 that have a remainder of 2 when divided by 13. Two things: i. n is a nonnegative integer ii. X is a positive integer less than 100 If so, n has to be 8 including 0.
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Re: How many positive integers less than 100 have a remainder of
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03 Jul 2011, 00:46
I dont understand how 2 can be included in the set. 2 div by 13 13) 2 ( > 13) 20 (0. > 13) 20 (0.1 Where do you get a reminder of 13? Thanks.
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Re: How many positive integers less than 100 have a remainder of
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11 Oct 2011, 08:49
+1 for 8.
similar to the previous explanation. x is positive & n is just a "non negative number" which means '0' is ok. So 0 through 7 = total 8.



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Re: How many positive integers less than 100 have a remainder of
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20 Jan 2018, 04:24
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