Permutation and Combination quiz

1. If none of the students are ambidextrous, what percentage of the 20 students in Mr. Henderson's class are left-handed? (1) Of the 12 girls in the class, 25% are left-handed.(2) 5 of the boys in the class are right-handed.

Statement 1 is sufficient

Statement 2 is sufficient

1 & 2 together

Each alone

None

Statement 1 tells us that 25% of the 12 girls in the class are left-handed. Since there are no ambidextrous students, this means that 3 girls in the class are left-handed.

Statement 2 tells us that 5 of the boys in the class are right-handed. Since there are no ambidextrous students, this means that all the boys in the class are right-handed.

Combining both statements, we know that there are 3 left-handed girls and all the boys are right-handed. Therefore, the percentage of left-handed students in Mr. Henderson's class is (3/20) x 100 = 15%.

Therefore, the answer is 1 & 2 together.

Explanation

Statement 1 tells us that 25% of the 12 girls in the class are left-handed. Since there are no ambidextrous students, this means that 3 girls in the class are left-handed.

Statement 2 tells us that 5 of the boys in the class are right-handed. Since there are no ambidextrous students, this means that all the boys in the class are right-handed.

Combining both statements, we know that there are 3 left-handed girls and all the boys are right-handed. Therefore, the percentage of left-handed students in Mr. Henderson's class is (3/20) x 100 = 15%.

Therefore, the answer is 1 & 2 together.

2. Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 40 films, and broke even on none of them, how many of their films were profitable?

18

19

20

21

22

In order to find the number of profitable films, we need to calculate the number of comedies and horror films separately. We know that 60% of the films were comedies, so 40% must be horror films. Since the studio made a total of 40 films, 40% of 40 is 16, which means there were 16 horror films.

Next, we can calculate the number of profitable comedies and horror films. 75% of the comedies were profitable, so 75% of 60% of 40 is 18. Similarly, 75% of the horror films were unprofitable, so 75% of 40% of 40 is 12.

To find the number of profitable films, we subtract the number of unprofitable films from the total number of films. 40 - 12 = 28. Therefore, 28 films were profitable.

Explanation

In order to find the number of profitable films, we need to calculate the number of comedies and horror films separately. We know that 60% of the films were comedies, so 40% must be horror films. Since the studio made a total of 40 films, 40% of 40 is 16, which means there were 16 horror films.

Next, we can calculate the number of profitable comedies and horror films. 75% of the comedies were profitable, so 75% of 60% of 40 is 18. Similarly, 75% of the horror films were unprofitable, so 75% of 40% of 40 is 12.

To find the number of profitable films, we subtract the number of unprofitable films from the total number of films. 40 - 12 = 28. Therefore, 28 films were profitable.

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Permutation And Combination Quiz