Who's seen "The Life of Pi" and "Finding Nemo?"

A 10th class was asked who had seen the movie "The Life of Pi" and who had seen, "Finding Nemo".

Twenty students had seen at least one of these movies. 20% of the students had seen neither of these movies.

How many students were in the class?


The answer is 25.

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10 solutions

Hello,easy 1,

as total students=x,

so,

20 +( 20/100).x = x

20 + (1/5).x=x

20(5) + x = 5x

4x=100 x=100/4=25...

thanks...

Lira Zabin
Mar 21, 2014

SAY, STUDENTS NUMBER IS X. X/5 STUDENTS DIDN'T WATCH ANY MOVIES.SO ,4X/5 STUDENTS WATCH THE MOVIE.SO, 4X/5=20 AND X=25

Draw a venn diagram with the class as the universal set and the people who have watched the movies as 2 sets.... It will make things simple. Answer is 25.

Nate Clegg
Oct 26, 2015

Let n be the total number of students in the class. Since we know that 20% of the total number of students haven't seen either movie, we can conclude that 80% of the total number of students have seen at least one movie.

We know that 20 students (or 80% of the total) had seen at least one of the movies: n × 0.8 = 20 n \times 0.8 = 20 But we want to know how many total students there are, so we need to solve for n .

First we divide both sides by 0.8 : n × 0.8 0.8 = 20 0.8 \frac{n \times 0.8}{0.8} = \frac{20}{0.8} Which simplifies to: n = 20 0.8 n = \frac{20}{0.8} 0.8 can be written as 80 100 \frac{80}{100} so if we substitute it in, we get n = 20 80 100 n = \frac{20}{\frac{80}{100}} or n = 20 × 100 80 n = 20 \times \frac{100}{80} This simplifies to n = 1 × 100 4 n = 1 \times \frac{100}{4}

This simplifies and we get n = 25 n = \boxed{25}

Abhimanyu Singh
Mar 19, 2014

This problem is simple set theory problem . Say A and B are two movies then
n(A) - n( A B A \cap B ) = no. of students seen movie A
n(B) - n( A B A \cap B ) = no. of students seen movie B
Thus, n(A) + n(B) - 2 × \times n( A B A \cap B ) = no. of students seen at least movie A or B
n( A B A \cap B ) = no. of students seen both movies A and B
and n( A B A \cup B ) = total no. of students




Let total no. of students = N, then
n( A B A \cup B ) = N
and n( A B A \cap B ) = N / 5
also n(A) + n(B) - 2 × \times n( A B A \cap B ) = 20

As n( A B A \cup B ) = n(A) + n(B) - n( A B A \cap B )
\Rightarrow n( A B A \cup B ) = n(A) + n(B) - 2 × \times n( A B A \cap B ) + n( A B A \cap B )
Thus, N = 20 + (N / 5)
So, N = 25 .

Palak Srivastava
Mar 15, 2014

let total no. of students be x.. since , 20 students were known. therefore, 20+20/100*x=25 there were 25 students in the class.....

Mehdi Khazane
Mar 12, 2014

20 students have seen at least one of the two movies, and 20% have seen neither the first nor the second. Which means that 20 constitutes 80% of the students of this class. If 20 is 80% the total number, then this total will be: 20+20/4=20+5=25

Vinit Dubey
Mar 10, 2014

20% students are not watching film, and in 20 students at least one of them watching film,that means 80% students are watching film. and 80% is equals to 20 students, therefore, 20% is equals to 5 students. and finally 20 + 5 = 25 students.

Shailesh Tiwari
Mar 9, 2014

it means 80% of student watch atleast 1of them so 80%of total student=2 the 20student so total student is 25

Muhamad Resiva
Mar 8, 2014

80% = 20 students who had watched movies ....

80/100 = 20

1/100 = 20/80 = 1/4

100/100 = 1/4 *100 = 25

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