In a survey of 100 families the number that read recent issues to a certain monthly magazine was found to be as follows: Issues Read Number of families September only 18 September and July 8 September but not August 23 September 26 July 48 July and August 8 None of the 3 months 24 Required i) Present the above information in a Venn diagram. (6mks) ii) How many families read the July issue if and only if they did not read the August issue? (2mks) iii) How many families read the August issue? (2mks) iv) How many families read the September and August issues but not the July issue? (2mks) b) Find the sum of the first 100terms of the arithmetic progression of 2,7,12,.. (4mks) c) Find the sum of the first 200 terms of the geometric progression 3,6,12,.. (4mks)
Answers
Answer:
According to the question,
a= 18 (September only 18 )-----(1)
a+b+d+f = 26 (september 26 )-----(2)
g+f+d+e = 48 (July 48 )-----(3)
d+e= 8 (July & August 8)-----(4)
d+f = 8 (September & July 8)-----(5)
a+f = 23 (September but not August 23)-----(6)
a+b+c+d+e+f+g = 76 (None of the 3 months 24)-----(7)
From (1) and (6), f=5---- (8)
From (8) and (5), d=3 --- (9)
From (9) and (4), e=5---- (10)
From (3), (8), (9) and (10), g= 35 --- (11)
From (2), (8), (9) and (1), b = 0
As only c is missing, putting values of all other unknowns in (7), we get c= 10.
Now let us answer the questions:
(a) August = b+c+d+e = 18
(b) Two consecutive issues will be either July August or August September = e + b = 5+ 0 = 5
(c) July minus August = g + f = 35 + 5 = 40
(d) Sept + Aug - July = b = 0.
Hope these are correct!
