number of athletes in the camp?

Question

I have weight range ( in pounds ) of athletes and corresponding number of athletes in a camp in a overlapping manner

http://img522.imageshack.us/my.php?image=scan0004wg8.jpg

i want to find MINIMUM number of athletes in the camp .

please explain the logic of your answer

Answer options

(1)46

(2)49

(3)51

(4)54

(5)55

Answer 1

The total number of athletes is 25+a+23, where "a" is the number of athletes from the interval 150
If sum of number of athletes with w=150 and w=160 is 22, then a=0.

Therefore minimum possible number of athletes is 48.

Answer 2

I liked this problem... I got an answer of 51. I started with the biggest number since that was the one that was going to have the biggest problem allocating... I said that 25 people were 145 pounds, which satisfied the first number... and then said the remaining 3 were 155 pounds to subtract 3 from the next two groups. Since the 150-160 group only has 19 people left, I put them at the extreme end at 160 to take 19 from the last two groups... the 155-165 group lost 3 and 19, so now only has 4 left, while the 160-170 group went from 23 to 4 as well... so the last 4 can be allocated at 165...
25+3+19+4 = 51

Answer 3

Looks to me like you want to know the MAXIMUM number of athletes in the camp, and that's 22!

Make the following table, and try to figure out the AVERAGE min and max weight of each athlete that you add (note you may add one or two athletes at a time).

In NO case do you get something consistent, e.g., to get from 22 to 23 athletes, we have to add an athlete from 380 to 390 pounds, which is too heavy.

To get from 23 to 25, we have to add two athletes weighing some NEGATIVE pounds.

To get from 25 to 26, we again have to add a very heavy athlete, and to get from 26 to 28, we have to add some baby athletes, too light for the weight range shown.

I say there is a MAXIMUM of 22 athletes in the camp.
# RANGE Tot Min Tot Max Min Added Max Added
22 150 160 3300 3520
23 160 170 3680 3910 380 390
25 140 150 3500 3750 -90 -80
26 155 165 4030 4290 530 540
28 145 155 4060 4340 15 25