I came across this question and I am posting it. Though it is a re-post but I need an additional clarification.
Q-1 In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
OA IS B
Here is an easier way of looking at this problem (and which has many applications toward other problems of the same type). Using the following formula A + B + C – AB – AC- BC – 2ABC + Neither = Total
...we want to find AB + AC + BC + ABC --> this is the same as the number of participants who liked at least one of the three products.
AB: # of participants who liked only A and B
AC: # of participants who liked only A and C
BC: # of participants who liked only B and C
ABC: # of participants who liked A, B and C only.
Filling this formula in with the given information we get:
50 + 30 + 20 – AB – AC – BC – 2(5) + 15 = 100
50 --> A
30 --> B
20 --> C
2(5) --> 2 * ABC
15 --> Neither (which is just 100-85 = neither)
Solving for AB, AC, and BC they all sum to 5 and when you add in the ABC portion, which is 5, we get 10 as the answer.
I hope this makes sense. Let me know if it doesn't.
Factorials were someone's attempt to make math look exciting!!!