ARITHMETIC – PROPERTIES OF NUMBERS?
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
Please provide your answer with step-by-step explanation and with easy-to-understand method.
Thanks and have a gorgeous day/night depending on where you live on this planet.
More Questions From This User See All
Answers & Comments
Verified answer
For n to be divisible by 35, it must be divisible by 5 AND 7 (since these are the only factors of 35 besides 1 and 35). Now, since the remainder is 1 when n is divided by 5, we get n = 5x + 1, where x is some integer. We also get n = 7y + 3, where y is also an integer. For n to be divisible by 5, we need n = 5j, where j is an integer; for n to be divisible by 7, we need n = 7k where k is an integer. What k value can we add to n = 7y + 3 to get an integer multiple of 7? What k value can we add to n = 5x + 1 to get an integer multiple of 5? If we add 4 to n, we get n = 7y + 3 + 4 = 7s, where s is an integer. We also get n = 5x + 1 + 4 = 5t, where t is an integer. So, the answer is B.