cpay3245 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
Here's one approach:
There's a nice rule that says,
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .
First we're told that when n is divided by 5, the remainder is 1.
So, possible values of n are 1, 6, 11, 16, 21, 26,
31, 36, 41, 46, 51, 56, 61,
66, 71, 76, etc.
Next we're told that when n is divided by 7, the remainder is 3.
So, possible values of n are 3, 10, 17, 24,
31, 38, 45, 52, 59,
66, 73, etc.
So, we can see that n could equal 31, or 66, or an infinite number of other values.
Important: Since the Least Common Multiple of 7 and 5 is 35, we can conclude that if we list the possible values of n, each value will be 35 greater than the last value.
So, n could equal 31, 66, 101, 136, and so on.
Notice that, if we take any of these values, we need to add 4 to it so that the sum will be a multiple of 35. So, the smallest value of k is 4 such that k+n is a multiple of 35.
Answer =
B
Cheers,
Brent
