Out of 210 interviews of IIM- Ahmedabad, 105 CAT crackers were offered tea by the interview panel, 50 were offered biscuits, and 56 were offered toffees. 32 CAT crackers were offered tea and biscuits, 30 were offered biscuits and toffees, and 45 were offered toffees and tea. What is the1) maximum and minimum number of CAT crackers who were offered all three snacks?2) maximum and minimum number of CAT crackers who were offered at least one snack?
Don't know whether it's a repeated question or not ? Anyways enjoy if you have not done it m/

1) 30,19,149,116
2) 45,12,123,116
3) 30,19,134,123
4) 45,12,149,116

• Let’s make the Venn diagram for this question. Since we want to assume least number of variables, we can see that assuming a variable for the number of students who were offered all three snacks will help us express all the other areas. Let the number of students who were offered all three snacks = x.
  
  
  
  In the above diagram, we have expressed all the areas in terms of x. To decide maximum value of x, we note that 32 - x, 45 - x and 30 - x will be zero or positive. Therefore, the maximum value of x will be 30. (30 is the lowest among 30, 32 and 45). To decide minimum value of x, we note than x - 19 and x – 12 will be zero or positive. Therefore, x cannot be less than 19 (19 is the higher number between 19 and 12).
  
  Therefore, maximum and minimum number of CAT crackers who were offered all three snacks = 30 and 19
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