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If N, C, and D are positive integers, what is the remainder

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If N, C, and D are positive integers, what is the remainder [#permalink] New post 06 Nov 2012, 17:35
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If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.
[Reveal] Spoiler: OA

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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 06 Nov 2012, 17:54
1. insufficient b/c D and C can be any number. adding +1 can change remainder completely.
ex: D =2 , C = 3 R = 2 ... D = 2+1 , C = 3+1 R = 3
2: sufficient b/c (ND + NC)/CN => ND/CN + NC/CN => ND/CN =>D/C + 1 => R5

answer: B
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 11 Sep 2013, 03:20
Can someone please help with a detailed explanation? Was able to get the answer right but don't really know how I arrived at it.

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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 14 Oct 2014, 12:11
1) insufficient
2) ND+NC/CN gives a remainder of 5.

ND + NC / CN = (D+C)/C

So we know that (D+C)/C gives a remainder of 5.

The idea here is that if you add any multiple of C to C then you will definitely get a multiple of C. For eg. 4 is a multiple of 2. So (4+2)/2 will give R=0.
In this case though we have a number added to C leaving a remainder of 5. This means that D is not divisible by C and that D must leave a remainder of 5. Eg. (5+0)/10 leaves a remainder of 5 . (5+10)/10 will leave a remainder of 5 also. So the remainder will always be in D in the equation (D+C). This means that D/C will also give us a remainder of 5. Sufficient.
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 28 Oct 2014, 11:10
Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

Please advise.
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 04 Nov 2014, 01:55
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.


Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Answer (B)


Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 04 Nov 2014, 20:03
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anupamadw wrote:
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.


Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Answer (B)


Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?


Actually it can take value 5 too. I will rewrite the solution given above soon.
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Re: If N, C, and D are positive integers, what is the remainder [#permalink] New post 04 Nov 2014, 20:15
Expert's post
nnitingarg wrote:
Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

Please advise.


In statement 1, say if C+1 = 8 and D+1 = 21, remainder is 5.
C = 7 and D = 20, remainder is 6.
Not sufficient alone.
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Re: If N, C, and D are positive integers, what is the remainder   [#permalink] 04 Nov 2014, 20:15
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