Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ... An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but an even number of odd numbers (like 1,3,5,7) add up to an even number. So if the sum is going to be exactly 400, then there will have to be an even number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8 Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 . Do you think that might be all there is to it ?
The time at which the cost for the services of the two companies would be in exactly 6 days. If we would compare the two charges, we would see that company A just charges 40 per day while B has a charge of 60, which is a standard fee, and a rate of 30 per day. So if we compute 40 x 6, we will have a total cost now of 240. If we compute 30 x 6, we will have a total cost now of 180 plus 60 which is the standard fee, and we will get 240. So in 6 days, the rates of the two companies would both accumulate to 240.