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When 777 is divided by positive integer n , the remainder is

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When 777 is divided by positive integer n , the remainder is [#permalink]  26 Oct 2008, 01:55
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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kris

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Re: Possibilities of n : Problem Solving [#permalink]  26 Oct 2008, 02:14
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, 02:38
sorry mate, but that's a wrong answer.
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Re: Possibilities of n : Problem Solving [#permalink]  26 Oct 2008, 02:42
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, 02:44
I think I missed 175
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Re: Possibilities of n : Problem Solving [#permalink]  26 Oct 2008, 03:37
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, 03:49
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, 04:29
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, 06:20
700 = 5*5*2*2*7
Factors greater than 77 are 100, 140, 175, 350, 700

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Re: Possibilities of n : Problem Solving [#permalink]  26 Oct 2008, 09:52
Yes, D is the answer. Thanks a lot.
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Re: Possibilities of n : Problem Solving   [#permalink] 26 Oct 2008, 09:52
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