akpareek wrote:In a survey conducted, it was found that 80% of the women surveyed were using atleast one of the three brands Lali, Ren and Ana. 40% of those surveyed were using Lali, 30% of the surveyed women were using Ren and 60% of the surveyed women were using Ana. 20% of the surveyed women use all the tree brands. What percentage of women surveyed use more than one of the given three brands?
Here is the formula for 3 overlapping groups:
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let T = 80%
Lali = 40.
Ren = 30.
Ana = 60.
Exactly 2 of the brands = x.
All 3 brands = 20.
Plugging these values into the formula, we get:
80 = 40 + 30 + 60 - x - 2(20)
80 = 90-x
x=10.
Since 10% use exactly 2 of the brands, and 20% use all 3 brands, the percentage who use more than one brand = 10+20 = 30.
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