is there any shorter way to calculate the number of integral points satisfying the inequality ??? or do we have to count the possibilities for y in integer co-ordinate of x ???
We could develop formulae for the simpler cases, Sahil….but then they would be rather specifically applicable. Also, in the heat of the test, a formula is the first thing that you would mess up generally 🙂 Personally, I prefer to count. Since there is usually a pretty visible pattern, it hardly takes time once you’ve practiced it a bit…
CAT-holics 
Hi J,
I’m getting 73 pairs for 7|x| + 3|y| < 28. Should it not be 73?
Yes, 79 – 6 boundary points. Edited, thanks!
regards
J
is there any shorter way to calculate the number of integral points satisfying the inequality ??? or do we have to count the possibilities for y in integer co-ordinate of x ???
We could develop formulae for the simpler cases, Sahil….but then they would be rather specifically applicable. Also, in the heat of the test, a formula is the first thing that you would mess up generally 🙂 Personally, I prefer to count. Since there is usually a pretty visible pattern, it hardly takes time once you’ve practiced it a bit…
regards
J