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# 51) How many integers from 0 to 50, inclusive, have a

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Senior Manager
Joined: 02 May 2004
Posts: 313
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51) How many integers from 0 to 50, inclusive, have a [#permalink]  25 Aug 2007, 22:56
51) How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A) 15
B) 16
C) 17
D) 18
E) 19
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Joined: 10 Jun 2007
Posts: 1465
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Kudos [?]: 133 [0], given: 0

Re: Inclusive Integer [#permalink]  25 Aug 2007, 23:02
jamesrwrightiii wrote:
51) How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A) 15
B) 16
C) 17
D) 18
E) 19

C.

consider from 4 to 50, you have 50/3 =~ 16 integers with remainder 1 when divided by 3.
Check the last one: 16*3 = 48 => 48+1 = 49, yes!
Then you have 1, which will also works.

So, total = 16+1 = 17
Senior Manager
Joined: 02 May 2004
Posts: 313
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Kudos [?]: 6 [0], given: 0

[#permalink]  25 Aug 2007, 23:35
Duh I forgot about 1...3 divides into 1 0 times but the remainder is 1.
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Re: Inclusive Integer [#permalink]  26 Aug 2007, 08:15
last term = first term + (n-1)d where d is the seperation factor

in our case

49=4+(n-1)3 <--- we are looking for number that when divide by 3 give remainder 1...

49-4+3=3n

48/3=16

so n=16...but remember its inclusive so you got to add 1...

17 it is

jamesrwrightiii wrote:
51) How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A) 15
B) 16
C) 17
D) 18
E) 19
Re: Inclusive Integer   [#permalink] 26 Aug 2007, 08:15
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# 51) How many integers from 0 to 50, inclusive, have a

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