Problem Solving

AAPL wrote:GMAT Paper Tests

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

OA B

Number of male students = 70% of 800 = 560;
Thus, the number of female students = 30% of 800 = 240;

Minimum number of female students who participate in a sport = 10% of 240 = 24;
Thus, the maximum number of female students who do not participate in a sport = 240 - 24 = 216;

Maximum number of male students who do not participate in a sport = 30% of 560 - 1 = 168 - 1 = 167;

Thus, the maximum possible number of students in School T who do not participate in a sport = 216 + 167 = 383

The correct answer: B

Hope this helps!

-Jay
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AAPL wrote:GMAT Paper Tests

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

OA B

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 and 0.3 x 560 = 168, 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

AAPL wrote:GMAT Paper Tests

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

OA B

The number of male students is 800 x 0.7 = 560, so there are 240 female students

Thus, at least 0.1 x 240 = 24 female students play a sport. In other words, at most 240 - 24 = 216 female students do not play a sport.

Fewer than 0.3 x 560 = 168 male students do not play a sport. In other words, at most 168 - 1 = 167 male students do not play a sport.

So we see that the maximum number of students who do not play a sport is 167 + 216 = 383.

Answer: B