Math Question - english translation issue

fogcity
Thu, 03 Nov 2011 15:19:17 +0000

To expand my previous post and answer …

A generic odd number is an even number plus 1 – i.e. 2n + 1 where n is an integer. So when n=0 you get 1, with n=1 you get 2*1 + 1 = 3, and then 5, 7, etc.

Two consecutive odd numbers are 2n + 1 and 2n + 3. So with n = 0 you get 1 and 3, and with n = 1 you get 3 and 5, and so on.

The equation (2n + 1)(2n + 3) < 400 has 10 possible answers – with n = 0 you have 13, with n =1 you have 3 * 5, etc. and finally with n = 9 you have 1921 which is barely less than 400. With n = 10 you get 2123 which is greater than 400.

So that’s how you get 10.

You can also just write it out: 1,3,5,7,9,11,13,15,17,19,21,23, … and look at the pairs 13,35,57, …1921. This way you’ll quickly see that the answer is 10.