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

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Manager
Joined: 17 Aug 2009
Posts: 163
How many integers from 0-50 have a remainder of 3 when divid  [#permalink]

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17 Dec 2009, 02:41
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15% (low)

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71% (00:59) correct 29% (01:02) wrong based on 313 sessions

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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
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Joined: 02 Sep 2009
Posts: 56369

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17 Dec 2009, 03:13
3
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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 $$5$$.

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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17 Dec 2009, 02:55
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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Joined: 18 Oct 2011
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06 Feb 2013, 04:01
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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Joined: 17 May 2013
Posts: 39
GMAT Date: 10-23-2013
Re: How many integers from 0-50 have a remainder of 3 when divid  [#permalink]

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09 Aug 2013, 00:12
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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Posts: 300
Re: How many integers from 0-50 have a remainder of 3 when divid  [#permalink]

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09 Aug 2013, 02:38
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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How many integers from 0-50 have a remainder of 3 when divid  [#permalink]

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26 Sep 2016, 12:57
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

3+9x<51
9x<48
x<5 1/3
5+1(for 3/9 remainder)=6
B.
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Re: How many integers from 0-50 have a remainder of 3 when divid  [#permalink]

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21 Aug 2018, 12:05
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Re: How many integers from 0-50 have a remainder of 3 when divid   [#permalink] 21 Aug 2018, 12:05
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