# Lesson: Integer Properties Strategies

## Comment on Integer Properties Strategies

### Wonderful module of summary

Wonderful module of summary of all topics. Very grateful and thankful to Brent sir for making GRE study so easy with better understanding ever. Feels like there is no chance of making mistakes with such robust concepts. ### Thanks for the kind words

Thanks for the kind words about the course.

Cheers,
Brent

### https://greprepclub.com/forum

https://greprepclub.com/forum/if-x-and-y-are-integers-greater-than-3-and-15y-11x-14957.html

Hej Brent,
could perhaps explain as to why y=13 in this example?
Thank you! In my solution, we learn that 4(2 – y) must be a multiple of 11?
Since 4 is NOT a multiple of 11, we can conclude that (2 - y) must be a multiple of 11

So, for example, it COULD be the case that (2 - y) = 11 (since 11 is a multiple of 11)
When we solve this equation for y we get, y = -9, but we can't use this y-value, because the given information tells us that y > 3.

Now let's test the case where (2 - y) = 22 (since 22 is also a multiple of 11)
When we solve this equation for y, we get y = -20, but we can't use this y-value either, because the given information tells us that y > 3.

Notice that, if we keep testing POSITIVE multiples of 11 (e.g., 11, 22, 33, 44, etc), the resulting y-value will always be negative, and this doesn't satisfy the condition that y > 3

So, let's try some NEGATIVE multiples of 11.

Let's first test the case where (2 - y) = -11 (since -11 is also a multiple of 11)
When we solve this equation for y, we get y = 13, and this y-value satisfies the condition that y > 3.

Now let's try another NEGATIVE multiple of 11.
Let's test the case where (2 - y) = -22 (since -22 is also a multiple of 11)
When we solve this equation for y, we get y = 24, and this y-value satisfies the condition that y > 3.

Notice, if we keep trying other negative multiples of 11 (e.g., -33, -44, -55, etc), the resulting y-values will get bigger and bigger and bigger.

Since we are looking for the SMALLEST possible value of y (such that y > 3), we can see that this occurs when (2 - y) = -11, and we get the corresponding y value of y = 13.

Does that help? 