QUESTION 7
- If
express y in terms of x. - A number of students were interviewed to find out which of the sporting activities they liked (football, boxing and volleyball). 70% of those interviewed liked football, 60% boxing and 45% volleyball. 45% liked football and boxing, 15% boxing and volleyball, 25% football and volleyball, 5% liked all the three sports and x% did not like any of the three sports.
- Draw a Venn diagram to illustrate this information.
- Use the diagram to find the percentage of students who liked:
- football and volleyball but not boxing;
- exactly two sports;
- none of the three sports.
Observation
The Chief Examiner reported that Candidates’ response was fair enough and showed some positivity that they had good understanding of Sets theory. However, they responded better in part(b) than part (a).
In part (a), they were expected to apply the laws of logarithm as follows:
. Then, simplifying to get yx2 = 216 which implies that 
In part (b) the responses were positive and right. They did as expected by first drawing the Venn diagram as shown
And then proceeded by football and volleyball but not boxing as 20%;
exactly two sports = 40% + 20% + 10% = 70% and finally none of the three sports by summing and equating to zero as follows :
5% + 5% + 10% +40% +10% + 20% + 5% + x% = 100%
Simplifying to get x + 95% = 100% and solving for x to get x = 5%.