1. In an examination conducted for 80 candidates, those who passed in mathematics were 17 more than those who passed science and 9 failed both subjects.14 candidates passed both subjects. I. Draw a venn diagram to illustrate this information II. How many students passed in mathematics? III. How many students passed in science? IV. How many passed exactly one subject?
I assume you can draw the Venn diagram. The universe is 80, the population outside the circles is 9, the population of the intersection of the circles is 14.
If you add M+S, you count twice the 14 who passed both.
so, M + S - 14 = 80-9 = 71
M + S = 85
M = 17+S
2S + 17 = 85
2S = 68
S = 34
so, M = 51
23,34
I. Here is a Venn diagram to illustrate the given information:
______________________________
| |
| Mathematics (M) |
| ________________________ |
| | | |
| | Passed Both | |
| | (14) | |
| |______________________| |
| / \ |
| / \ |
| \/ \/
| ^ \ / |
| \ \___________________/ |
| \__ __________________ |
| | Passed in | |
| | Mathematics | |
| | only | |
| | (x + 17) | |
| |___________________| |
| | | |
| Failed | Failed | |
| Both | Mathematics |
| (9) | (y) |
|________|_____________|
II. To determine the number of students who passed in mathematics, we add the number of students who passed both subjects and those who passed in mathematics only:
Number of students passed in mathematics = Number who passed both + Number who passed in math only
Number of students passed in mathematics = 14 + (x + 17)
III. To determine the number of students who passed in science, we add the number of students who passed both subjects and those who passed in mathematics only:
Number of students passed in science = Number who passed both + Number who passed in math only + Number who failed both
Number of students passed in science = 14 + (x + 17) + 9
IV. To determine the number of students who passed exactly one subject, we subtract the number of students who passed both subjects from the total number of students who passed in either mathematics or science:
Number of students who passed exactly one subject = (Number who passed in math only) + (Number who passed in science only)
Number of students who passed exactly one subject = (x + 17) + (9 - 14)
Please note that the values of 'x' and 'y' are not given, so we cannot determine the exact number of students for questions II, III, and IV without additional information.
I. To draw a Venn diagram to illustrate this information, we need to label the three regions of the diagram. Let's use M for Mathematics, S for Science, and U for students who failed both subjects (unsuccessful students).
So, the first step is to draw two overlapping circles for Mathematics and Science. Label the intersection of the two circles as passing in both subjects (14 students). Then label the remaining sections outside the intersection as students who passed only in Mathematics (M - 14) and students who passed only in Science (S - 14). Finally, label the area outside both circles as unsuccessful students (U - 9).
II. To find the number of students who passed in Mathematics, we need to add the number of students who passed only in Mathematics (M - 14) and those who passed in both subjects (14). So, the total number of students who passed in Mathematics would be (M - 14) + 14.
III. Similarly, to find the number of students who passed in Science, we add the number of students who passed only in Science (S - 14) plus those who passed in both subjects (14). So, the total number of students who passed in Science would be (S - 14) + 14.
IV. To find the number of students who passed in exactly one subject, we need to sum the number of students who passed only in Mathematics (M - 14) and those who passed only in Science (S - 14). So, the total number of students who passed in exactly one subject would be (M - 14) + (S - 14).
It's important to note that the given information does not provide the actual values of M (number of students who passed in Mathematics) and S (number of students who passed in Science), so we cannot determine the specific values for questions II, III, and IV with the given information. However, we have described the steps to calculate them once we have the required information.