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Re: How many positive integers less than 100 have a remainder of [#permalink]

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21 Sep 2009, 21:42

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\(\frac{X-2}{13} = n\) where n is a non-negative 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.

Re: How many positive integers less than 100 have a remainder of [#permalink]

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22 Sep 2009, 18:20

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?

Re: How many positive integers less than 100 have a remainder of [#permalink]

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21 Oct 2009, 22:50

AKProdigy87 wrote:

\(\frac{X-2}{13} = n\) where n is a non-negative 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 non-negative integer ii. X is a positive integer less than 100

If so, n has to be 8 including 0.
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