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How many integers from 0-50 have a remainder of 3 when divid

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How many integers from 0-50 have a remainder of 3 when divid [#permalink] New post 17 Dec 2009, 01:41
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How many integers from 0-50 have a remainder of 3 when divided by 9?

A. 5
B. 6
C. 7
D. 8
E. 9
[Reveal] Spoiler: OA
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Re: Remainder Problem [#permalink] New post 17 Dec 2009, 02:13
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zaarathelab wrote:
How many integers from 0-50 have a remainder of 3 when divided by 9?

A. 5
B 6
C 7
D 8
E 9


A remainder of 3 when divided by 9 --> n=9q+3, where q is an integer \geq{0}.

9q+3<50 --> q<5\frac{2}{9}, hence q can take 6 values from 0 to 5.

Answer: B (6).

Or, one can just manually list the numbers of the form n=9q+3, which are less than 50: 3, 12, 21, 30, 39, and 48. Total of 6 numbers.
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Re: Remainder Problem [#permalink] New post 17 Dec 2009, 01:55
All numbers should be of the form 9c+3 where c is a constant.

Min is 3 for c=0
Max in 48 for c=5

The answer should be B = 6
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Re: Remainder Problem [#permalink] New post 06 Feb 2013, 03:01
Range of numbers is 50-0+1= 51.
Possible remainders= 0,1,2,3,4,5,6,7,8
51/9 gives a quotient 5 and a remainder 6. This means that after completing 5 rounds from 0 to 8 ,it found numbers with remainders from 0 to 5 and this has 1 extra count for remainder 3.Hence it is 5+1=6
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Re: How many integers from 0-50 have a remainder of 3 when divid [#permalink] New post 08 Aug 2013, 23:12
The first number when divided by 9 leaves a remainder of 3 is 3.
The last number below 50 when divided by 9 leaves a remainder of 3 is 48
so
(48 - 3)/9 + 1 = 6

Ans : B
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Re: How many integers from 0-50 have a remainder of 3 when divid [#permalink] New post 09 Aug 2013, 01:38
zaarathelab wrote:
How many integers from 0-50 have a remainder of 3 when divided by 9?

A. 5
B. 6
C. 7
D. 8
E. 9

....
-9-18-27-36-45-
- = number of integers have a remainder of 3
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Asif vai.....

Re: How many integers from 0-50 have a remainder of 3 when divid   [#permalink] 09 Aug 2013, 01:38
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