Seventy percent of the 800 students in School T are male...

[BTGmoderatorLU]

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

The OA is B.

I'm confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

[Vincen]

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

The OA is B.

I'm confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

Hello LUANDATO.

We have 800 students.

Seventy percent are male, this implies that 560 students are male and therefore 240 are females.

1. At least ten percent of the female students in School T participate in a sport; this implies that the minimum number of females that participate in a sport is: 10%*240=24.

2. Fewer than thirty percent of the male students in School T do not participate in a sport; this implies that the maximum of males that do not participate in a sport less than is: 30%*560=168. This tells us that the maximum is 167 males that do not participate in a sport.

3. Now, from 2. we know that the minimum number of males that participate in a sport is: 560-167=393.

Using 3. and 2. we get that the minimum number of students that participate in a sport is: 393+24=417.

In other words, the maximum number of students that do not participate in a sport is 800-417=383.

Therefore, the correct answer is B.

I hope it helps.

[Scott@TargetTestPrep]

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

We see that the number of male students in School T = 0.7 x 800 = 560 and, thus, the number of female students = 800 - 560 = 240.

Since at least 10% of the female students in School T participate in a sport, at most 90% of them do not. Since we want to determine the maximum possible number of students in School T who do not participate in a sport, we can say 90% of the female students, i.e., 0.9 x 240 = 216 female students do not participate in a sport. Likewise, since fewer than 30% of the male students in School T, which makes 0.3 x 560 = 168 students, do not participate in a sport, we can assume 168 - 1 = 167 male students do not participate in a sport.

Thus the total number of students who do not participate in a sport is at most 216 + 167 = 383.

Answer: B