Bunuel wrote:
SOLUTION
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
Positive integer n is divided by 5, the remainder is 1 -->\(n=5q+1\) , where\(q\) is the quotient --> 1, 6, 11, 16, 21, 26,31 , ...
Positive integer n is divided by 7, the remainder is 3 -->\(n=7p+3\) , where\(p\) is the quotient --> 3, 10, 17, 24,31 ,....
There is a way to derive general formula for \(n\) (of a type \(n=mx+r\), where \(x\) is divisor and \(r\) is a remainder) based on above two statements:
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