kidderek wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?
A. 216
B. 383
C. 384
D. 416
E. 417
This problem can best be tackled via the max/min principle. To wit, if you want to maximize a value, you should minimize some other value or constraint. In this case, we want to maximize the number of students who do not play a sport, so we should minimize the number of students who do play a sport.
We know that at least 10% of female students out of 240 total female students play a sport. So the minimum value here is 24. Thus, 240-24 = 216 female students do not play a sport at most.
We know that fewer than 30% of male students do not play a sport, so we want to maximize this value. Since students are humans and thus must be integers, the smallest value here is 167<3/10*560 -1. If we did not reduce by 1, then the number of male students who do not play a sport would be equal to 30% of male students, not less than 30% of male students. It plays a role in the answer choices.
240+ 167 = 383, the maximum number of students who do not play a sport.