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# OG Quant 2nd Edition #68 in PS

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OG Quant 2nd Edition #68 in PS [#permalink]  20 Apr 2011, 18:25
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

A - 3
B - 4
C -12
D - 32
E - 35

The OG explanation is too cumbersome. does anyone have a simpler explanation?
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Kudos [?]: 228 [0], given: 34

Re: OG Quant 2nd Edition #68 in PS [#permalink]  20 Apr 2011, 19:04
n = 5p + 1 = 1,6,11,16,21,26,31,

n = 7q + 3 = 3,10,17,24,31

So n = 35r + 31 (LCM of co-efficients + 1st common number)

So if r = 0, n = 31, and we need to add 4 to make it 35

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Kudos [?]: 3 [0], given: 1

Re: OG Quant 2nd Edition #68 in PS [#permalink]  20 Apr 2011, 19:51
smodak wrote:
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

A - 3
B - 4
C -12
D - 32
E - 35

The OG explanation is too cumbersome. does anyone have a simpler explanation?

number-properties-og-question-112111.html#p907830
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Kudos [?]: 4 [0], given: 3

Re: OG Quant 2nd Edition #68 in PS [#permalink]  20 Apr 2011, 20:13
mniyer wrote:
smodak wrote:
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

A - 3
B - 4
C -12
D - 32
E - 35

The OG explanation is too cumbersome. does anyone have a simpler explanation?

number-properties-og-question-112111.html#p907830

Thanks. That explains it very well.
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Re: OG Quant 2nd Edition #68 in PS [#permalink]  30 Apr 2011, 22:16
n= 5a+1= 7b+3
5a-7b = 2

(k+n)/35 = integer

starting with k = 12 and checking for k+n = 35, 70

n= 23 which is not possible.
k = 4, n = 31 which means a= 6 and b = 4.
Hence B.
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Re: OG Quant 2nd Edition #68 in PS   [#permalink] 30 Apr 2011, 22:16
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