Among 18 students in a room, 7 study mathematics, 10 study science, and 10 study computer programming. Also, 3 study mathematics
and science, 4 study mathematics and computer programming, and 5 study science and computer programming. We know that 1 student studies all three subjects. How many of these students study none of the three subjects?
2 answers:
Answer:
2 students study none of the subjects.
Step-by-step explanation:
Consider the attached venn diagram. First, we place that 1 student studies the three subjects. Then, we notice that 3 students study math and science, then 2 students study math and science only, since we have 1 that studies the three subjects. In the same fashion, we have that 3 students study Math and computer programming only (since they are 4 in total). Note that since 7 students study math, and we already have 6 students in our count in the math subject this implies that 1 student studies only math (the total number of students inside the math circle must add to 7).
We also have that 4 students study science and computer programming only. Which implies that we must have 3 students that study science only (10 students that study science in total) and 2 students study computer programming (for a total of 10 students). The total number of students that study none is the total number of students (18) minus the amount of students that is inside the circles (16) which is 2.
Answer: 3 students study none of the three subjects
Step-by-step explanation:
The Venn diagram representing the situation is shown in the attached photo.
M represents the sub set of mathematics students.
S represents the sub set of science students.
CP represents the sub set of computer programming students.
From the diagram,
The number of students studying mathematics and science only is
3 - 1 = 2
The number of students studying mathematics and computer programming only is
4 - 1 = 3
The number of students studying science and computer programming only is
5 - 1 = 4
The number of students studying mathematics only is
7 - (2 + 1 + 3) = 1
The number of students studying mathematics only is
10 - (2 + 1 + 4) = 3
The number of students studying computer programming only is
10 - (3 + 1 + 4) = 2
Let x represent the number of students that study none of the three subjects. Since the total number of students is 18, it means that
2 + 3 + 4 + 1 + 3 + 2 + x = 18
15 + x = 18
x = 18 - 15 = 3
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Answer: 11 is the required number that always divides such differences for the following types of numbers.
Step-by-step explanation:
Take any 3 - digit number, say, 325
On reversing its digit it becomes, 523
On subtracting the smaller of the two numbers from the larger,
we can see that 198 is an even number.
take another number say, 629
On reversing its digit, it becomes = 926
On subtracting , we get that
But 297 is not an even number.
But there is one common in both the cases is that both the differences are divisible by 11.
Hence, 11 is the required number that always divides such differences for the following types of numbers.
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EXPLANATION
We want to simplify
We multiply the first fraction by the reciprocal of the second fraction to obtain,
We cancel the common factors to get,
This gives us,