# Lesson: Introduction to Divisibility

## Comment on Introduction to Divisibility

### Hi Brent Could you explain

Hi Brent Could you explain the x=ky statement at 5:46 ### You bet.

You bet.

"x is divisible by y" is the SAME AS "x = ky for some integer k"

For example, since 20 is divisible by 2, we can also say that 20 = 2k for some integer k (in this case k = 10)

Since 33 is divisible by 11, we can also say that 33 = 11k for some integer k (in this case k = 3)

Since 42 is divisible by 6, we can also say that 42 = 6k for some integer k (in this case k = 7)

Does that help?

Cheers,
Brent

### https://in.edugain.com/forum

https://in.edugain.com/forum/Question/3155/if-4y-3x-5-what-is-the-smallest-integer-value-of-x-for-which-y-100-/

Hi Brent!

In this question, when I use 101 as the value of y, I get x as 133. However, Barron's answer guide says that its 132. I was wondering whether my logic was correct or no?

4y-3x=5;

4(101)-3x=5
3x=399
x=133

This is how I solved the equation. Just because y > 100, we can't say that y = 101
It could be the case that y = 100.1 or 100.2 or....

Here's my solution:
Given: 4y - 3x = 5
Add 3x to both sides: 4y = 3x + 5
Solve: y = (3x + 5)/4

We want y to be GREATER THAN 100
So, let's first see what it takes for y to EQUAL 100
Set y = 100 to get: 100 = (3x + 5)/4
Multiply both side by 4 to get: 400 = 3x + 5
So, 3x = 395
Solve: x = 395/3
Rewrite as: x = 131 2/3

So, when x = 131 2/3, y EQUALS 100
So, when x is greater than 131 2/3, y will be GREATER THAN 100

132 is the smallest INTEGER that's greater than 131 2/3, so the correct answer is 132

Cheers,
Brent

### Is there any divisibility

Is there any divisibility rules for numbers 11-15? To figure out if a number is divisible by these #s? For instance, i had a hard time figuring out that 180 is divisible by 12 and missed it as a factor. ### There is a divisibility rule

There is a divisibility rule for 11, but it is not tested on the GRE.
On test day, you need to know the divisibility rules for 2, 3, 4, 5, 6, 9, and 10

That said, we can combine some of the rules to make up other rules.
For example, if a number is divisible by 15, that it must be divisible by 3 and by 5.
So, for example, we know that 10035 must be divisible by 15, because we can confirm that 10035 is divisible by both 3 and 5.

Likewise, if a number is divisible by 12, that it must be divisible by 3 and by 4.
So, for example, we know that 11232 must be divisible by 12, because we can confirm that it's divisible by both 3 and 4.