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## Comment on

Integer Properties Strategies## Wonderful module of summary

## Thanks for the kind words

Thanks for the kind words about the course.

Cheers,

Brent

## https://greprepclub.com/forum

Hej Brent,

could perhaps explain as to why y=13 in this example?

Thank you!

## Question link: https:/

Question link: https://greprepclub.com/forum/if-x-and-y-are-integers-greater-than-3-and...

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?

## You've made it perfectly

Thank you Brent!

It is a rare occurrence that one can explain things in such a coherent way as you do.

## That's kind of you to say.

That's kind of you to say. Thanks!

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