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

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Manager
Joined: 06 Nov 2008
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How many integers from 0 to 50, inclusive, have a remainder [#permalink]

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11 Nov 2008, 20:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Director
Joined: 14 Aug 2007
Posts: 733
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11 Nov 2008, 20:45
haichao wrote:
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.17

an= a1 + (n-1)d

Here an = 49, a1= 1 and d =3.

n= 17
SVP
Joined: 30 Apr 2008
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11 Nov 2008, 21:58
Because there will be a remainder of 1 for every three numbers, take the total number of numbers and divide by 3 and that's the answer. Here that is 50 - 0, but add 1 because 0 is inclusive. This results in 51. 51 / 3 = 17.

Same answer as posted previously, but a less "scientific" method.

I'm just curious to see if this would apply to any other similar problem, such as how many integers from 0 to 50, inclusive have a remainder of 2 when divided by 4?

Again, 51 numbers, and there will be a remainder of 2 every 4 integers. The answer would be 51/4? = 12 (don't count remainder on this division.

2
6
10
14
18
22
26
30
34
38
42
46
50

NOpe, this didn't work because the answer would actually be 13.

haichao wrote:
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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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

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Re: remainder--27   [#permalink] 11 Nov 2008, 21:58
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