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How many positive integers less than 100 have a remainder of 2 when

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How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 26 Oct 2010, 22:02
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How many positive integers less than 100 have a remainder of 2 when divided by 13?

A. 6
B. 7
C. 8
D. 9
E. 10

15, 28,41,54,67,80,93 = 7
but the set includes 2 which makes answer choice C right ? why 2 is included in the set ??

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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 26 Oct 2010, 22:08
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shrive555 wrote:
How many positive integers less than 100 have a remainder of 2 when divided by 13?

6
7
8
9
10

15, 28,41,54,67,80,93 = 7
but the set includes 2 which makes answer choice C right ? why 2 is included in the set ??


We have to include 2 also.As 13*0 + 2 =2

If somebody says to divide 2 by 13 ,we will be telling we have 0 quotient and remainder as 2.

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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 27 Oct 2010, 17:24
I've mentioned it before on this forum, but the answer to the question above is hopefully clear if you remember how you first learned quotients and remainders. If you have 23 apples and 6 children, and you want to give each child the same number of apples, you can give each child at most 3 apples, and then you'll have 5 apples left over. So when we divide 23 by 6, the quotient is 3 and the remainder is 5.

If instead you have 2 apples and 13 children, then you can give each child 0 apples, and you have 2 left over. So when you divide 2 by 13, the quotient is 0 and the remainder is 2.
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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 27 Oct 2010, 17:31
i'll remember apples and children
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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 14 Jul 2017, 00:44
Highest multiple of 13<100 is 91 which is of the form 13*7, hence we have 7 multiples plus 2 in each that leaves a remainder of 2 when divided by 13. Also when 13 divides 2 it leaves a remainder of 2. In total we have 8 integers<100 in this situation.
Please advise if the approach is relevant.
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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 16 Jul 2017, 17:45
shrive555 wrote:
How many positive integers less than 100 have a remainder of 2 when divided by 13?

A. 6
B. 7
C. 8
D. 9
E. 10


The first positive integer that has a remainder of 2 when divided by 13 is 2. The greatest positive integer less than 100 that has a remainder of 2 when divided by 13 is 93.

So, the total number of numbers that have a remainder of 2 when divided by 13 is (93 - 2)/13 + 1 = 7 + 1 = 8.

Answer: C
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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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New post 16 Jul 2017, 19:58
shrive555 wrote:
How many positive integers less than 100 have a remainder of 2 when divided by 13?

A. 6
B. 7
C. 8
D. 9
E. 10



2+13x<100
13x<98
x<7.5
x=7
1+7=8
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Re: How many positive integers less than 100 have a remainder of 2 when  [#permalink]

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Re: How many positive integers less than 100 have a remainder of 2 when   [#permalink] 06 Feb 2019, 21:45
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