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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://gre.myprepclub.com/forum
Hej Brent,
could perhaps explain as to why y=13 in this example?
Thank you!
Question link: https:/
Question link: https://gre.myprepclub.com/forum/if-x-and-y-are-integers-greater-than-3-...
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!