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
When positive integer n is divided by 5, the remainder is 1.
The smallest possible value of n that satisfies the statement above is the given remainder of 1.
To determine the other possible values of n, just keep adding multiples of the divisor 5:
1,6,11,16,21,26,31...
When positive integer n is divided by 7, the remainder is 3.
The smallest possible value of n that satisfies the statement above is the given remainder of 3.
To determine the other possible values of n, just keep adding multiples of the divisor 7:
3,10,17,24,31...
The smallest value included in both lists is n=31.
Now examine the answer choices.
When the correct answer choice is added to n=31, the sum will be a multiple of 35.
We can quickly see that the smallest possible value that will work is k=4 in answer choice
B:
n+k = 31+4 = 35.
The correct answer is
B.
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