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When 777 is divided by positive integer n , the remainder is [#permalink]
 26 Oct 2008, 02:55
When 777 is divided by positive integer n , the remainder is 77. How many possibilities are there for n? a) 2 b) 3 c) 4 d) 5 e) 6 Thanks
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 03:14
krishan wrote: When 777 is divided by positive integer n , the remainder is 77. How many possibilities are there for n?
a) 2
b) 3
c) 4
d) 5
e) 6
Thanks n has to be greater than 77 and it should divide 700 completely leaving a reminder of 77 n can be - 100, 350,700.
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 03:38
sorry mate, but that's a wrong answer.
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 03:42
krishan wrote: sorry mate, but that's a wrong answer. I knew I'd be wrong 
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 03:44
I think I missed 175
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 04:37
here are the factors: 700, 350, 175, 100, 140. I factored 700 as : 700 x 1 : 350 x 2 : 175 x 4 : 35 x 20 : 7 x 100 : 1 x 700 (this completes the cycle) The numbers which are multiple of 700 and greater than 77 are: 700, 350, 175, 100. One I didn't get was 140. I am not sure if this is the right way to arrive at a solution.
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 04:49
krishan wrote: here are the factors: 700, 350, 175, 100, 140.
I factored 700 as
: 700 x 1
: 350 x 2
: 175 x 4
: 35 x 20
: 7 x 100
: 1 x 700 (this completes the cycle)
The numbers which are multiple of 700 and greater than 77 are: 700, 350, 175, 100.
One I didn't get was 140. I am not sure if this is the right way to arrive at a solution. I agree, there has to be a better way ....
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 05:29
amitdgr wrote: krishan wrote: here are the factors: 700, 350, 175, 100, 140.
I factored 700 as
: 700 x 1
: 350 x 2
: 175 x 4
: 35 x 20
: 7 x 100
: 1 x 700 (this completes the cycle)
The numbers which are multiple of 700 and greater than 77 are: 700, 350, 175, 100.
One I didn't get was 140. I am not sure if this is the right way to arrive at a solution. I agree, there has to be a better way .... I used the same method: multiples of 700 greater than 77. However, I think you missed 140 * 5. Therefore answer is 700, 350, 175, 140, 100.
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 07:20
700 = 5*5*2*2*7
Factors greater than 77 are 100, 140, 175, 350, 700
D.5 must be the answer
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Re: Possibilities of n : Problem Solving [#permalink]
26 Oct 2008, 10:52
Yes, D is the answer. Thanks a lot.
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Re: Possibilities of n : Problem Solving
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26 Oct 2008, 10:52
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