I know the answer but how would I show how I got to my answer

Question

If n is a positive integer which is never divisible 5?

a)n+5

b)3n+4

c)4n+3

d)5n+1

Answer 1

If n is a positive integer which is never divisible 5?
a)n+5
b)3n+4
c)4n+3
d)5n+1

 

To say "never," we must not have any cases where it is divisible by 5.

 

(a) is divisible by 5 when n=5 (or any multiple of 5)

(b) is divisible by 5 when n=7 (and others)

(c) is divisible by 5 when n=3 (and others)

(d) is never divisible by 5; because 5n is always divisible by 5 and 1 more makes it not divisible by 5

Answer 2

Keep in mind what divisible means. If you divide a number by 5, you're asking "how many times can 5 go into this number?"

 

If we considered 5n + 1 for different integers n, they would look like

 

1, 6, 11, 16, 21, 26, 31, 36, ... etc.

 

These are all numbers that end in a 1 or a 6 which means they can't be divisible by 5. 

 

Looking at an expression like 5n + 1, you can note that 5 goes into this n times with a remainder of 1. 

 

---

 

Look at the term "5n". What this means is "multiple of 5". If you add one to a multiple of five, it is no longer a multiple of five. To get to another multiple of 5, you have to go up at least 5 more. 

 

Like 26 can't be a multiple of 5, because I know that 25 is and to get to the next multiple of 5, I need to add at least 5. 26 is only one away.

 

Don't forget that multiplication is repeated addition.

 

(e.g. 4x5 = "five four times" = 5 + 5 + 5 + 5)

 

It's important to recognize this because it tells you that you get multiples of a number by counting by it. You get multiples of 5 by starting at 5 and counting by 5. Any number that falls in between what you get when you count by 5s can't be a multiple of 5. So any number that can be expressed as a multiple of 5 that you then add 1 to is too close to that multiple of 5 to be one itself.

Answer 3

I get answer d.

 

There are many ways of making n + 5 divisible by 5. Pick any multiple of 5 for n. So, a cannot be the answer.

 

For b, if you make n = 2, for instance, then you have 3*2 + 4 = 10, which h is divisible by 5.

 

For c, you can make n = 3, then you get 15 which is divisible by 5.

 

But, for part d, whatever you make n, 5n will always be a multiple of 5. But, when you add 1, 5n + 1 will never be divisible by 5.