This question is confusing me so if anyone could explain in detail I would really appreciate it. I don't understand why it isn't solved the same way as practice question 6... in that question you had Brand A + Brand B + both brands + neither brands = 200 and the answer was 15... on this question though, it is leaving out AND part (11) out of the results. Why isn't it 24 + 1.5x + 11 + × = 84?!?!
The underlying concept behind both the questions is the same. However, there is slight change in the way the information has been provided. Let me explain with a venn diagram.
In the questions with two overlapping sets a + b + c + d = Total no. of objects
. In both the questions, the same concept has been used.
However there is a difference between the way information has been provided. Let's see how.
In this question let's assume group 1 = parents who volunteer to supervise children and group 2 =parents who bring refreshements
The question gives us the value of no. of parents who volunteer to supervise children = 35. Please note that this includes parents who only supervise children as well as parents who supervise children and bring refreshments both. So, a + b = 35. Also, parents who volunteer to supervise children as well as bring refreshment = b = 11. So, we can write the value of a = 24.
Since we are also told that no. of parents who volunteered to bring refreshment is 1.5 times the no. of parents who neither volunteered to supervise children nor bring refreshment, we can write b + c = 1.5d. Note here that parents who volunteered to bring refreshments include parents who only bring refreshments as well as parents who bring refreshments and supervise children both.
Since a + b + c + d = Total number of parents = 84, we can write 24 + (b + c) + d = 84. Since b + c = 1.5d, 24 + 2.5d = 84 which gives us the value of d = 24 and hence b + c = 1.5*24 = 36.For every set question, please keep an eye on the use of word "Only"
. In this case the question asked the number of parents who volunteered to bring refreshments which also included parents who volunteered to supervise the children as well as bring refreshments.
In practice question no. 6
, note the use of word "Only". The question there uses the term extensively to segregate the users of the brands. For your reference, in Q6 we can write the value of a = 60, b = x, c = 3x and d = 80 assuming group 1 as users of brand A and group 2 as users of brand B.
Hope its clear! Let me know if you still have trouble at any point of the explanation.