1. So far John has earned .70 * 100 * N or 70N points.
With the next exam he will have (N+1) exams and needs to average .72*100 points. Therefore he needs a total of 72(N+1) points.
His score on the last test needs to be the difference between those two figures:
72(N+1) - 70N = 2N + 72

Another way to look at it is that John is down 2 points for every test he has taken so far. (Net down = 2N). To reach a 72 average he has to score 72 on the last test PLUS make up for the points missed so far so: 72 + 2N.

2. Each of 15 players plays the other 14 players twice. That might look like 15*14*2, BUT - you need to divide by 2 since a game with players A and B is the same as a game with players B and A. So (15*14*2)/2 = 210

3. Sam earns $300. That represents $1.60 for every $2 Jason earned. So (Jason/2)*1.6 = Sam. That means .8*Jason = $300. So Jason earned $375. But Jason earned $1.5 for every dollar Jim earned so we have to divide Jason's earnings by 1.5. We find that Jim earned $250.

4. To be divisible by 2 and 7, an integer must be a multiple of 14. Between 11 and 55 we have 14, 28, and 42. Total = 3

5. This is unclear. I assume you are looking for the largest value of N such that 98*98 is divisible by 7^N. If so, you attack it this way. 98 = 7*7*2. Therefore 98*98 = (7*7*2)*(7*7*2) = (7^4)*(2^2). Answer = 4.

About part 5

I think the question meant 98^98 and not 98*98 .

I'd say factors of 98 are 7x7x2

therefore, we have (7x7x2)^(98)

or 7^98 x 7^98 x 2^98

or 7^(2*98) x 2^98

or 7^196 x 2^98

so 7^196 would be the largest number and 196 will be the largest value of N which can divide 98^98.

I hope I interpreted the question right.

If the question is in fact 98^98 you are correct.