When the positive integer y is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer z is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of y-z? Choose the correct choice from the following options:
A) 12
B) 24
C) 35
D) 16
E) 30
If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:   n = 5y + 3   n = 7z + 4   I will need to check for the smallest such number.   I put z= 1. n = 11. Is it of the form 5y + 3? No.   Put z= 2. n = 18. Is it of the form 5y + 3? Yes.   When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.   Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder   Next will be 35*2 + 18   and so on...   Difference between such numbers will be a multiple of 35 so your answer is 35.   your answer is 35
<result>C</result>
When the positive integer y is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer z is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of y-z?