This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions to questions 7 to 13 based on the provided Venn diagram. Question 7: How many pupils like football only? Step 1: Identify the region representing "football only". This is the part of the TRIANGLE that does not overlap with the RECTANGLE (Tennis Ball) or the CIRCLE (Athletics). Step 2: From Figure 1, this region contains the number 3. The correct option is C. 3. Question 8: How many pupils like tennis ball only? Step 1: Identify the region representing "tennis ball only". This is the part of the RECTANGLE that does not overlap with the TRIANGLE (Football) or the CIRCLE (Athletics). Step 2: From Figure 1, this region contains the number 1. The correct option is A. 1. Question 9: How many pupils like athletics only? Step 1: Identify the region representing "athletics only". This is the part of the CIRCLE that does not overlap with the TRIANGLE (Football) or the RECTANGLE (Tennis Ball). Step 2: From Figure 1, this region contains the number 7. The correct option is C. 7. Question 10: How many pupils like all the three games? Step 1: Identify the region where all three shapes (TRIANGLE, RECTANGLE, CIRCLE) overlap. Step 2: From Figure 1, this central region contains the number 4. The correct option is B. 4. Question 11: How many pupils like athletics and football only? Step 1: Identify the region where the CIRCLE (Athletics) and the TRIANGLE (Football) overlap, but not the RECTANGLE (Tennis Ball). Step 2: The overlap between the CIRCLE and TRIANGLE includes regions 4 and 5. Region 4 also includes Tennis Ball. Therefore, the region for athletics and football only is 5. The correct option is B. 5. Question 12: How many pupils like football and tennis ball only? Step 1: Identify the region where the TRIANGLE (Football) and the RECTANGLE (Tennis Ball) overlap, but not the CIRCLE (Athletics). Step 2: The overlap between the TRIANGLE and RECTANGLE includes regions 2 and 4. Region 4 also includes Athletics. Therefore, the region for football and tennis ball only is 2. The correct option is D. 2. Question 13: How many pupils like athletics and tennis ball only? Step 1: Identify the region where the CIRCLE (Athletics) and the RECTANGLE (Tennis Ball) overlap, but not the TRIANGLE (Football). Step 2: The overlap between the CIRCLE and RECTANGLE includes regions 4 and 6. Region 4 also includes Football. Therefore, the region for athletics and tennis ball only is 6. The correct option is B. 6. Drop the next question.